diff --git a/Doc/library/textwrap.rst b/Doc/library/textwrap.rst
--- a/Doc/library/textwrap.rst
+++ b/Doc/library/textwrap.rst
@@ -25,6 +25,9 @@
    Optional keyword arguments correspond to the instance attributes of
    :class:`TextWrapper`, documented below.  *width* defaults to ``70``.
 
+   See the :meth:`TextWrapper.wrap` method for additional details on how
+   :func:`wrap` behaves.
+
 
 .. function:: fill(text, width=70, **kwargs)
 
@@ -167,15 +170,18 @@
 
    .. attribute:: drop_whitespace
 
-      (default: ``True``) If true, whitespace that, after wrapping, happens to
-      end up at the beginning or end of a line is dropped (leading whitespace in
-      the first line is always preserved, though).
+      (default: ``True``) If true, whitespace at the beginning and ending of
+      every line (after wrapping but before indenting) is dropped.
+      Whitespace at the beginning of the paragraph, however, is not dropped
+      if non-whitespace follows it.  If whitespace being dropped takes up an
+      entire line, the whole line is dropped.
 
 
    .. attribute:: initial_indent
 
       (default: ``''``) String that will be prepended to the first line of
-      wrapped output.  Counts towards the length of the first line.
+      wrapped output.  Counts towards the length of the first line.  The empty
+      string is not indented.
 
 
    .. attribute:: subsequent_indent
@@ -236,8 +242,9 @@
 
       Wraps the single paragraph in *text* (a string) so every line is at most
       :attr:`width` characters long.  All wrapping options are taken from
-      instance attributes of the :class:`TextWrapper` instance. Returns a list
-      of output lines, without final newlines.
+      instance attributes of the :class:`TextWrapper` instance.  Returns a list
+      of output lines, without final newlines.  If the wrapped output is an
+      empty string or empty line, the list returned is empty.
 
 
    .. method:: fill(text)
diff --git a/Lib/test/test_textwrap.py b/Lib/test/test_textwrap.py
--- a/Lib/test/test_textwrap.py
+++ b/Lib/test/test_textwrap.py
@@ -22,7 +22,7 @@
             result = []
             for i in range(len(textin)):
                 result.append("  %d: %r" % (i, textin[i]))
-            result = '\n'.join(result)
+            result = "\n".join(result) if result else "  no lines"
         elif isinstance(textin, str):
             result = "  %s\n" % repr(textin)
         return result
@@ -66,6 +66,15 @@
                          "I'm glad to hear it!"])
         self.check_wrap(text, 80, [text])
 
+    def test_empty_string(self):
+        # Check that wrapping the empty string returns an empty list.
+        self.check_wrap("", 6, [])
+        self.check_wrap("", 6, [], drop_whitespace=False)
+
+    def test_empty_string_with_initial_indent(self):
+        # Check that the empty string is not indented.
+        self.check_wrap("", 6, [], initial_indent="++")
+        self.check_wrap("", 6, [], initial_indent="++", drop_whitespace=False)
 
     def test_whitespace(self):
         # Whitespace munging and end-of-sentence detection
@@ -331,7 +340,32 @@
                          ["blah", " ", "(ding", " ", "dong),",
                           " ", "wubba"])
 
-    def test_initial_whitespace(self):
+    def test_drop_whitespace_false(self):
+        # Check that drop_whitespace=False preserves whitespace.
+        # SF patch #1581073
+        text = " This is a    sentence with     much whitespace."
+        self.check_wrap(text, 10,
+                        [" This is a", "    ", "sentence ",
+                         "with     ", "much white", "space."],
+                        drop_whitespace=False)
+
+    def test_drop_whitespace_false_whitespace_only(self):
+        # Check that drop_whitespace=False preserves a whitespace-only string.
+        self.check_wrap("   ", 6, ["   "], drop_whitespace=False)
+
+    def test_drop_whitespace_false_whitespace_only_with_indent(self):
+        # Check that a whitespace-only string gets indented (when
+        # drop_whitespace is False).
+        self.check_wrap("   ", 6, ["     "], drop_whitespace=False,
+                        initial_indent="  ")
+
+    def test_drop_whitespace_whitespace_only(self):
+        # Check drop_whitespace on a whitespace-only string.
+        self.check_wrap("  ", 6, [])
+
+    def test_drop_whitespace_leading_whitespace(self):
+        # Check that drop_whitespace does not drop leading whitespace (if
+        # followed by non-whitespace).
         # SF bug #622849 reported inconsistent handling of leading
         # whitespace; let's test that a bit, shall we?
         text = " This is a sentence with leading whitespace."
@@ -340,13 +374,27 @@
         self.check_wrap(text, 30,
                         [" This is a sentence with", "leading whitespace."])
 
-    def test_no_drop_whitespace(self):
-        # SF patch #1581073
-        text = " This is a    sentence with     much whitespace."
-        self.check_wrap(text, 10,
-                        [" This is a", "    ", "sentence ",
-                         "with     ", "much white", "space."],
+    def test_drop_whitespace_whitespace_line(self):
+        # Check that drop_whitespace skips the whole line if a non-leading
+        # line consists only of whitespace.
+        text = "abcd    efgh"
+        # Include the result for drop_whitespace=False for comparison.
+        self.check_wrap(text, 6, ["abcd", "    ", "efgh"],
                         drop_whitespace=False)
+        self.check_wrap(text, 6, ["abcd", "efgh"])
+
+    def test_drop_whitespace_whitespace_only_with_indent(self):
+        # Check that initial_indent is not applied to a whitespace-only
+        # string.  This checks a special case of the fact that dropping
+        # whitespace occurs before indenting.
+        self.check_wrap("  ", 6, [], initial_indent="++")
+
+    def test_drop_whitespace_whitespace_indent(self):
+        # Check that drop_whitespace does not drop whitespace indents.
+        # This checks a special case of the fact that dropping whitespace
+        # occurs before indenting.
+        self.check_wrap("abcd efgh", 6, ["  abcd", "  efgh"],
+                        initial_indent="  ", subsequent_indent="  ")
 
     def test_split(self):
         # Ensure that the standard _split() method works as advertised