diff --git a/Include/abstract.h b/Include/abstract.h
--- a/Include/abstract.h
+++ b/Include/abstract.h
@@ -535,9 +535,6 @@
 
 
 
-     PyAPI_FUNC(int) PyBuffer_ToContiguous(void *buf, Py_buffer *view,
-                                           Py_ssize_t len, char fort);
-
      PyAPI_FUNC(int) PyBuffer_FromContiguous(Py_buffer *view, void *buf,
                                              Py_ssize_t len, char fort);
 
diff --git a/Include/memoryobject.h b/Include/memoryobject.h
--- a/Include/memoryobject.h
+++ b/Include/memoryobject.h
@@ -25,6 +25,8 @@
                                                int flags);
 #ifndef Py_LIMITED_API
 PyAPI_FUNC(PyObject *) PyMemoryView_FromBuffer(Py_buffer *info);
+PyAPI_FUNC(int) PyBuffer_ToContiguous(void *buf, Py_buffer *view,
+                                      Py_ssize_t len, char order);
 #endif
 PyAPI_FUNC(PyObject *) PyMemoryView_GetContiguous(PyObject *base,
                                                   int buffertype,
diff --git a/Lib/test/test_buffer.py b/Lib/test/test_buffer.py
--- a/Lib/test/test_buffer.py
+++ b/Lib/test/test_buffer.py
@@ -53,6 +53,11 @@
     'f':0, 'd':0, 'P':0
 }
 
+# NumPy does not have 'n' or 'N':
+if numpy_array:
+    del NATIVE['n']
+    del NATIVE['N']
+
 if struct:
     try:
         # Add "qQ" if present in native mode.
@@ -855,11 +860,49 @@
                            is_contiguous(result, 'F') and order == 'C':
                             # The flattened list is already in C-order.
                             expected = ndarray(flattened, shape=shape, format=ff)
-                            contig = get_contiguous(result, PyBUF_READ, order)
+
                     contig = get_contiguous(result, PyBUF_READ, order)
                     self.assertEqual(contig.tobytes(), b)
                     self.assertTrue(cmp_contig(contig, expected))
 
+                    if ndim == 0:
+                        continue
+
+                    nmemb = len(flattened)
+                    ro = 0 if readonly else ND_WRITABLE
+
+                    ### See comment in test_py_buffer_to_contiguous for an
+                    ### explanation why these tests are valid.
+
+                    # To 'C'
+                    contig = py_buffer_to_contiguous(result, 'C', PyBUF_FULL_RO)
+                    self.assertEqual(len(contig), nmemb * itemsize)
+                    initlst = [struct.unpack_from(fmt, contig, n*itemsize)[0]
+                               for n in range(nmemb)]
+
+                    y = ndarray(initlst, shape=shape, flags=ro, format=fmt)
+                    self.assertEqual(memoryview(y), memoryview(result))
+
+                    # To 'F'
+                    contig = py_buffer_to_contiguous(result, 'F', PyBUF_FULL_RO)
+                    self.assertEqual(len(contig), nmemb * itemsize)
+                    initlst = [struct.unpack_from(fmt, contig, n*itemsize)[0]
+                               for n in range(nmemb)]
+
+                    y = ndarray(initlst, shape=shape, flags=ro|ND_FORTRAN,
+                                format=fmt)
+                    self.assertEqual(memoryview(y), memoryview(result))
+
+                    # To 'A'
+                    contig = py_buffer_to_contiguous(result, 'A', PyBUF_FULL_RO)
+                    self.assertEqual(len(contig), nmemb * itemsize)
+                    initlst = [struct.unpack_from(fmt, contig, n*itemsize)[0]
+                               for n in range(nmemb)]
+
+                    f = ND_FORTRAN if is_contiguous(result, 'F') else 0
+                    y = ndarray(initlst, shape=shape, flags=f|ro, format=fmt)
+                    self.assertEqual(memoryview(y), memoryview(result))
+
         if is_memoryview_format(fmt):
             try:
                 m = memoryview(result)
@@ -1805,6 +1848,9 @@
                         self.assertEqual(mvlist, ylist)
 
                 if numpy_array:
+                    # XXX NumPy (as far as it compiles with 3.3) currently
+                    # segfaults here. Wait for a stable 3.3 compatible version.
+                    continue
                     shape = t[3]
                     if 0 in shape:
                         continue # http://projects.scipy.org/numpy/ticket/1910
@@ -1884,6 +1930,9 @@
                     self.assertEqual(mr.tolist(), yrlist)
 
                 if numpy_array:
+                    # XXX NumPy (as far as it compiles with 3.3) currently
+                    # segfaults here. Wait for a stable 3.3 compatible version.
+                    continue
                     if 0 in lshape or 0 in rshape:
                         continue # http://projects.scipy.org/numpy/ticket/1910
 
@@ -2020,6 +2069,246 @@
         nd = ndarray(list(range(12)), shape=[2,2,3], format='L')
         self.assertEqual(hash(nd), hash(nd.tobytes()))
 
+    def test_py_buffer_to_contiguous(self):
+
+        # The requests are used in _testbuffer.c:py_buffer_to_contiguous
+        # to generate buffers without full information for testing.
+        requests = (
+            # distinct flags
+            PyBUF_INDIRECT, PyBUF_STRIDES, PyBUF_ND, PyBUF_SIMPLE,
+            # compound requests
+            PyBUF_FULL, PyBUF_FULL_RO,
+            PyBUF_RECORDS, PyBUF_RECORDS_RO,
+            PyBUF_STRIDED, PyBUF_STRIDED_RO,
+            PyBUF_CONTIG, PyBUF_CONTIG_RO,
+        )
+
+        # no buffer interface
+        self.assertRaises(TypeError, py_buffer_to_contiguous, {}, 'F',
+                          PyBUF_FULL_RO)
+
+        # scalar, read-only request
+        nd = ndarray(9, shape=(), format="L", flags=ND_WRITABLE)
+        for order in ['C', 'F', 'A']:
+            for request in requests:
+                b = py_buffer_to_contiguous(nd, order, request)
+                self.assertEqual(b, nd.tobytes())
+
+        # zeros in shape
+        nd = ndarray([1], shape=[0], format="L", flags=ND_WRITABLE)
+        for order in ['C', 'F', 'A']:
+            for request in requests:
+                b = py_buffer_to_contiguous(nd, order, request)
+                self.assertEqual(b, b'')
+
+        nd = ndarray(list(range(8)), shape=[2, 0, 7], format="L",
+                     flags=ND_WRITABLE)
+        for order in ['C', 'F', 'A']:
+            for request in requests:
+                b = py_buffer_to_contiguous(nd, order, request)
+                self.assertEqual(b, b'')
+
+        ### One-dimensional arrays are trivial, since Fortran and C order
+        ### are the same.
+
+        # one-dimensional
+        for f in [0, ND_FORTRAN]:
+            nd = ndarray([1], shape=[1], format="h", flags=f|ND_WRITABLE)
+            ndbytes = nd.tobytes()
+            for order in ['C', 'F', 'A']:
+                for request in requests:
+                    b = py_buffer_to_contiguous(nd, order, request)
+                    self.assertEqual(b, ndbytes)
+
+            nd = ndarray([1, 2, 3], shape=[3], format="b", flags=f|ND_WRITABLE)
+            ndbytes = nd.tobytes()
+            for order in ['C', 'F', 'A']:
+                for request in requests:
+                    b = py_buffer_to_contiguous(nd, order, request)
+                    self.assertEqual(b, ndbytes)
+
+        # one-dimensional, non-contiguous input
+        nd = ndarray([1, 2, 3], shape=[2], strides=[2], flags=ND_WRITABLE)
+        ndbytes = nd.tobytes()
+        for order in ['C', 'F', 'A']:
+            for request in [PyBUF_STRIDES, PyBUF_FULL]:
+                b = py_buffer_to_contiguous(nd, order, request)
+                self.assertEqual(b, ndbytes)
+
+        nd = nd[::-1]
+        ndbytes = nd.tobytes()
+        for order in ['C', 'F', 'A']:
+            for request in requests:
+                try:
+                    b = py_buffer_to_contiguous(nd, order, request)
+                except BufferError:
+                    continue
+                self.assertEqual(b, ndbytes)
+
+        ###
+        ### Multi-dimensional arrays:
+        ###
+        ### The goal here is to preserve the logical representation of the
+        ### input array but change the physical representation if necessary.
+        ###
+        ### _testbuffer example:
+        ### ====================
+        ###
+        ###    C input array:
+        ###    --------------
+        ###       >>> nd = ndarray(list(range(12)), shape=[3, 4])
+        ###       >>> nd.tolist()
+        ###       [[0, 1, 2, 3],
+        ###        [4, 5, 6, 7],
+        ###        [8, 9, 10, 11]]
+        ###
+        ###    Fortran output:
+        ###    ---------------
+        ###       >>> py_buffer_to_contiguous(nd, 'F', PyBUF_FULL_RO)
+        ###       >>> b'\x00\x04\x08\x01\x05\t\x02\x06\n\x03\x07\x0b'
+        ###
+        ###    The return value corresponds to this input list for
+        ###    _testbuffer's ndarray:
+        ###       >>> nd = ndarray([0,4,8,1,5,9,2,6,10,3,7,11], shape=[3,4],
+        ###                        flags=ND_FORTRAN)
+        ###       >>> nd.tolist()
+        ###       [[0, 1, 2, 3],
+        ###        [4, 5, 6, 7],
+        ###        [8, 9, 10, 11]]
+        ###
+        ###    The logical array is the same, but the values in memory are now
+        ###    in Fortran order.
+        ###
+        ### NumPy example:
+        ### ==============
+        ###    _testbuffer's ndarray takes lists to initialize the memory.
+        ###    Here's the same sequence in NumPy:
+        ###
+        ###    C input:
+        ###    --------
+        ###       >>> nd = ndarray(buffer=bytearray(list(range(12))),
+        ###                        shape=[3, 4], dtype='B')
+        ###       >>> nd
+        ###       array([[ 0,  1,  2,  3],
+        ###              [ 4,  5,  6,  7],
+        ###              [ 8,  9, 10, 11]], dtype=uint8)
+        ###
+        ###    Fortran output:
+        ###    ---------------
+        ###       >>> fortran_buf = nd.tostring(order='F')
+        ###       >>> fortran_buf
+        ###       b'\x00\x04\x08\x01\x05\t\x02\x06\n\x03\x07\x0b'
+        ###       
+        ###       >>> nd = ndarray(buffer=fortran_buf, shape=[3, 4],
+        ###                        dtype='B', order='F')
+        ###
+        ###       >>> nd
+        ###       array([[ 0,  1,  2,  3],
+        ###              [ 4,  5,  6,  7],
+        ###              [ 8,  9, 10, 11]], dtype=uint8)
+        ###
+
+        # multi-dimensional, contiguous input
+        lst = list(range(12))
+        for f in [0, ND_FORTRAN]:
+            nd = ndarray(lst, shape=[3, 4], flags=f|ND_WRITABLE)
+            if numpy_array:
+                na = numpy_array(buffer=bytearray(lst),
+                                 shape=[3, 4], dtype='B',
+                                 order='C' if f == 0 else 'F')
+
+            # 'C' request
+            if f == ND_FORTRAN: # 'F' to 'C'
+                x = ndarray(transpose(lst, [4, 3]), shape=[3, 4],
+                            flags=ND_WRITABLE)
+                expected = x.tobytes()
+            else:
+                expected = nd.tobytes()
+            for request in requests:
+                try:
+                    b = py_buffer_to_contiguous(nd, 'C', request)
+                except BufferError:
+                    continue
+
+                self.assertEqual(b, expected)
+
+                # Check that output can be used as the basis for constructing
+                # a C array that is logically identical to the input array.
+                y = ndarray([v for v in b], shape=[3, 4], flags=ND_WRITABLE)
+                self.assertEqual(memoryview(y), memoryview(nd))
+
+                if numpy_array:
+                    self.assertEqual(b, na.tostring(order='C'))
+
+            # 'F' request
+            if f == 0: # 'C' to 'F'
+                x = ndarray(transpose(lst, [3, 4]), shape=[4, 3],
+                            flags=ND_WRITABLE)
+            else:
+                x = ndarray(lst, shape=[3, 4], flags=ND_WRITABLE)
+            expected = x.tobytes()
+            for request in [PyBUF_FULL, PyBUF_FULL_RO, PyBUF_INDIRECT,
+                            PyBUF_STRIDES, PyBUF_ND]:
+                try:
+                    b = py_buffer_to_contiguous(nd, 'F', request)
+                except BufferError:
+                    continue
+                self.assertEqual(b, expected)
+
+                # Check that output can be used as the basis for constructing
+                # a Fortran array that is logically identical to the input array.
+                y = ndarray([v for v in b], shape=[3, 4], flags=ND_FORTRAN|ND_WRITABLE)
+                self.assertEqual(memoryview(y), memoryview(nd))
+
+                if numpy_array:
+                    self.assertEqual(b, na.tostring(order='F'))
+
+            # 'A' request
+            if f == ND_FORTRAN:
+                x = ndarray(lst, shape=[3, 4], flags=ND_WRITABLE)
+                expected = x.tobytes()
+            else:
+                expected = nd.tobytes()
+            for request in [PyBUF_FULL, PyBUF_FULL_RO, PyBUF_INDIRECT,
+                            PyBUF_STRIDES, PyBUF_ND]:
+                try:
+                    b = py_buffer_to_contiguous(nd, 'A', request)
+                except BufferError:
+                    continue
+
+                self.assertEqual(b, expected)
+
+                # Check that output can be used as the basis for constructing
+                # an array with order=f that is logically identical to the input
+                # array.
+                y = ndarray([v for v in b], shape=[3, 4], flags=f|ND_WRITABLE)
+                self.assertEqual(memoryview(y), memoryview(nd))
+
+                if numpy_array:
+                    self.assertEqual(b, na.tostring(order='A'))
+
+        # multi-dimensional, non-contiguous input
+        nd = ndarray(list(range(12)), shape=[3, 4], flags=ND_WRITABLE|ND_PIL)
+
+        # 'C'
+        b = py_buffer_to_contiguous(nd, 'C', PyBUF_FULL_RO)
+        self.assertEqual(b, nd.tobytes())
+        y = ndarray([v for v in b], shape=[3, 4], flags=ND_WRITABLE)
+        self.assertEqual(memoryview(y), memoryview(nd))
+
+        # 'F'
+        b = py_buffer_to_contiguous(nd, 'F', PyBUF_FULL_RO)
+        x = ndarray(transpose(lst, [3, 4]), shape=[4, 3], flags=ND_WRITABLE)
+        self.assertEqual(b, x.tobytes())
+        y = ndarray([v for v in b], shape=[3, 4], flags=ND_FORTRAN|ND_WRITABLE)
+        self.assertEqual(memoryview(y), memoryview(nd))
+
+        # 'A'
+        b = py_buffer_to_contiguous(nd, 'A', PyBUF_FULL_RO)
+        self.assertEqual(b, nd.tobytes())
+        y = ndarray([v for v in b], shape=[3, 4], flags=ND_WRITABLE)
+        self.assertEqual(memoryview(y), memoryview(nd))
+
     def test_memoryview_construction(self):
 
         items_shape = [(9, []), ([1,2,3], [3]), (list(range(2*3*5)), [2,3,5])]
diff --git a/Modules/_testbuffer.c b/Modules/_testbuffer.c
--- a/Modules/_testbuffer.c
+++ b/Modules/_testbuffer.c
@@ -2397,6 +2397,49 @@
     return PyMemoryView_GetContiguous(obj, (int)type, ord);
 }
 
+/* PyBuffer_ToContiguous() */
+static PyObject *
+py_buffer_to_contiguous(PyObject *self, PyObject *args)
+{
+    PyObject *obj;
+    PyObject *order;
+    PyObject *ret = NULL;
+    int flags;
+    char ord;
+    Py_buffer view;
+    char *buf = NULL;
+
+    if (!PyArg_ParseTuple(args, "OOi", &obj, &order, &flags)) {
+        return NULL;
+    }
+
+    if (PyObject_GetBuffer(obj, &view, flags) < 0) {
+        return NULL;
+    }
+
+    ord = get_ascii_order(order);
+    if (ord == CHAR_MAX) {
+        goto out;
+    }
+
+    buf = PyMem_Malloc(view.len);
+    if (buf == NULL) {
+        PyErr_NoMemory();
+        goto out;
+    }
+
+    if (PyBuffer_ToContiguous(buf, &view, view.len, ord) < 0) {
+        goto out;
+    }
+
+    ret = PyBytes_FromStringAndSize(buf, view.len);
+
+out:
+    PyBuffer_Release(&view);
+    PyMem_XFree(buf);
+    return ret;
+}
+
 static int
 fmtcmp(const char *fmt1, const char *fmt2)
 {
@@ -2734,6 +2777,7 @@
     {"get_pointer", get_pointer, METH_VARARGS, NULL},
     {"get_sizeof_void_p", (PyCFunction)get_sizeof_void_p, METH_NOARGS, NULL},
     {"get_contiguous", get_contiguous, METH_VARARGS, NULL},
+    {"py_buffer_to_contiguous", py_buffer_to_contiguous, METH_VARARGS, NULL},
     {"is_contiguous", is_contiguous, METH_VARARGS, NULL},
     {"cmp_contig", cmp_contig, METH_VARARGS, NULL},
     {NULL, NULL}
diff --git a/Objects/abstract.c b/Objects/abstract.c
--- a/Objects/abstract.c
+++ b/Objects/abstract.c
@@ -445,62 +445,6 @@
     }
 }
 
-  /* view is not checked for consistency in either of these.  It is
-     assumed that the size of the buffer is view->len in
-     view->len / view->itemsize elements.
-  */
-
-int
-PyBuffer_ToContiguous(void *buf, Py_buffer *view, Py_ssize_t len, char fort)
-{
-    int k;
-    void (*addone)(int, Py_ssize_t *, const Py_ssize_t *);
-    Py_ssize_t *indices, elements;
-    char *dest, *ptr;
-
-    if (len > view->len) {
-        len = view->len;
-    }
-
-    if (PyBuffer_IsContiguous(view, fort)) {
-        /* simplest copy is all that is needed */
-        memcpy(buf, view->buf, len);
-        return 0;
-    }
-
-    /* Otherwise a more elaborate scheme is needed */
-
-    /* XXX(nnorwitz): need to check for overflow! */
-    indices = (Py_ssize_t *)PyMem_Malloc(sizeof(Py_ssize_t)*(view->ndim));
-    if (indices == NULL) {
-        PyErr_NoMemory();
-        return -1;
-    }
-    for (k=0; k<view->ndim;k++) {
-        indices[k] = 0;
-    }
-
-    if (fort == 'F') {
-        addone = _Py_add_one_to_index_F;
-    }
-    else {
-        addone = _Py_add_one_to_index_C;
-    }
-    dest = buf;
-    /* XXX : This is not going to be the fastest code in the world
-             several optimizations are possible.
-     */
-    elements = len / view->itemsize;
-    while (elements--) {
-        addone(view->ndim, indices, view->shape);
-        ptr = PyBuffer_GetPointer(view, indices);
-        memcpy(dest, ptr, view->itemsize);
-        dest += view->itemsize;
-    }
-    PyMem_Free(indices);
-    return 0;
-}
-
 int
 PyBuffer_FromContiguous(Py_buffer *view, void *buf, Py_ssize_t len, char fort)
 {
diff --git a/Objects/bytearrayobject.c b/Objects/bytearrayobject.c
--- a/Objects/bytearrayobject.c
+++ b/Objects/bytearrayobject.c
@@ -789,7 +789,7 @@
         size = view.len;
         if (PyByteArray_Resize((PyObject *)self, size) < 0) goto fail;
         if (PyBuffer_ToContiguous(self->ob_bytes, &view, size, 'C') < 0)
-                goto fail;
+            goto fail;
         PyBuffer_Release(&view);
         return 0;
     fail:
diff --git a/Objects/bytesobject.c b/Objects/bytesobject.c
--- a/Objects/bytesobject.c
+++ b/Objects/bytesobject.c
@@ -2591,7 +2591,6 @@
         new = PyBytes_FromStringAndSize(NULL, view.len);
         if (!new)
             goto fail;
-        /* XXX(brett.cannon): Better way to get to internal buffer? */
         if (PyBuffer_ToContiguous(((PyBytesObject *)new)->ob_sval,
                                   &view, view.len, 'C') < 0)
             goto fail;
diff --git a/Objects/memoryobject.c b/Objects/memoryobject.c
--- a/Objects/memoryobject.c
+++ b/Objects/memoryobject.c
@@ -438,15 +438,17 @@
         view->strides[i] = view->strides[i-1] * view->shape[i-1];
 }
 
-/* Copy src to a C-contiguous representation. Assumptions:
+/* Copy src to a contiguous representation. order is one of 'C', 'F' (Fortran)
+   or 'A' (Any). Assumptions: src has PyBUF_FULL information, src->ndim >= 1,
    len(mem) == src->len. */
 static int
-buffer_to_c_contiguous(char *mem, Py_buffer *src)
+buffer_to_contiguous(char *mem, Py_buffer *src, char order)
 {
     Py_buffer dest;
     Py_ssize_t *strides;
     int ret;
 
+    assert(src->ndim >= 1);
     assert(src->shape != NULL);
     assert(src->strides != NULL);
 
@@ -456,12 +458,22 @@
         return -1;
     }
 
-    /* initialize dest as a C-contiguous buffer */
+    /* initialize dest */
     dest = *src;
     dest.buf = mem;
-    /* shape is constant and shared */
+    /* shape is constant and shared: the logical representation of the
+       array is unaltered. */
+
+    /* The physical representation determined by strides (and possibly
+       suboffsets) may change. */
     dest.strides = strides;
-    init_strides_from_shape(&dest);
+    if (order == 'C' || order == 'A') {
+        init_strides_from_shape(&dest);
+    }
+    else {
+        init_fortran_strides_from_shape(&dest);
+    }
+
     dest.suboffsets = NULL;
 
     ret = copy_buffer(&dest, src);
@@ -922,6 +934,57 @@
 
 
 /****************************************************************************/
+/*                         Previously in abstract.c                         */
+/****************************************************************************/
+
+typedef struct {
+    Py_buffer view;
+    Py_ssize_t array[1];
+} Py_buffer_full;
+
+int
+PyBuffer_ToContiguous(void *buf, Py_buffer *src, Py_ssize_t len, char order)
+{
+    Py_buffer_full *fb = NULL;
+    int ret;
+
+    assert(order == 'C' || order == 'F' || order == 'A');
+
+    if (len != src->len) {
+        PyErr_SetString(PyExc_ValueError,
+            "PyBuffer_ToContiguous: len != view->len");
+        return -1;
+    }
+
+    if (PyBuffer_IsContiguous(src, order)) {
+        memcpy((char *)buf, src->buf, len);
+        return 0;
+    }
+
+    /* buffer_to_contiguous() assumes PyBUF_FULL */
+    fb = PyMem_Malloc(sizeof *fb + 3 * src->ndim * (sizeof *fb->array));
+    if (fb == NULL) {
+        PyErr_NoMemory();
+        return -1;
+    }
+    fb->view.ndim = src->ndim;
+    fb->view.shape = fb->array;
+    fb->view.strides = fb->array + src->ndim;
+    fb->view.suboffsets = fb->array + 2 * src->ndim;
+
+    init_shared_values(&fb->view, src);
+    init_shape_strides(&fb->view, src);
+    init_suboffsets(&fb->view, src);
+
+    src = &fb->view;
+
+    ret = buffer_to_contiguous(buf, src, order);
+    PyMem_Free(fb);
+    return ret;
+}
+
+
+/****************************************************************************/
 /*                           Release/GC management                          */
 /****************************************************************************/
 
@@ -1889,7 +1952,7 @@
     if (bytes == NULL)
         return NULL;
 
-    if (buffer_to_c_contiguous(PyBytes_AS_STRING(bytes), src) < 0) {
+    if (buffer_to_contiguous(PyBytes_AS_STRING(bytes), src, 'C') < 0) {
         Py_DECREF(bytes);
         return NULL;
     }
@@ -2423,7 +2486,7 @@
                 PyErr_NoMemory();
                 return -1;
             }
-            if (buffer_to_c_contiguous(mem, view) < 0) {
+            if (buffer_to_contiguous(mem, view, 'C') < 0) {
                 PyMem_Free(mem);
                 return -1;
             }