diff --git a/Doc/library/textwrap.rst b/Doc/library/textwrap.rst
--- a/Doc/library/textwrap.rst
+++ b/Doc/library/textwrap.rst
@@ -22,8 +22,13 @@
    *width* characters long.  Returns a list of output lines, without final
    newlines.
 
-   Optional keyword arguments correspond to the instance attributes of
-   :class:`TextWrapper`, documented below.  *width* defaults to ``70``.
+   The optional keyword arguments correspond to the keyword arguments to the
+   :class:`TextWrapper` class constructor.  *width* defaults to ``70``.
+
+   See the :class:`TextWrapper` class for information on the optional keyword
+   arguments and :meth:`TextWrapper.wrap` for additional details on how
+   :func:`wrap` behaves.
+
 
 
 .. function:: fill(text, width=70, **kwargs)
@@ -167,15 +172,18 @@
 
    .. 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 first line, however, is not dropped
+      (provided that non-whitespace follows it on that line).  If a line is
+      entirely whitespace, the whole line is removed.
 
 
    .. 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
@@ -239,6 +247,8 @@
       instance attributes of the :class:`TextWrapper` instance. Returns a list
       of output lines, without final newlines.
 
+      This method returns an empty list if the wrapped output is an empty line.
+
 
    .. 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 +66,8 @@
                          "I'm glad to hear it!"])
         self.check_wrap(text, 80, [text])
 
+    def test_empty_string(self):
+        self.check_wrap("", 10, [])
 
     def test_whitespace(self):
         # Whitespace munging and end-of-sentence detection
@@ -331,7 +333,8 @@
                          ["blah", " ", "(ding", " ", "dong),",
                           " ", "wubba"])
 
-    def test_initial_whitespace(self):
+    def test_drop_whitespace__initial_whitespace(self):
+        # Check that drop_whitespace does not drop initial 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."
@@ -340,7 +343,32 @@
         self.check_wrap(text, 30,
                         [" This is a sentence with", "leading whitespace."])
 
-    def test_no_drop_whitespace(self):
+    def test_drop_whitespace__initial_whitespace_line(self):
+        # Check that drop_whitespace drops initial whitespace if that
+        # whitespace is on a line by itself.
+        text = "    abcd"
+        self.check_wrap(text, 6, ["++    ", "abcd"], initial_indent="++",
+                        drop_whitespace=False)
+        self.check_wrap(text, 6, ["++abcd"], initial_indent="++")
+
+    def test_drop_whitespace__before_indenting(self):
+        # Check 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.
+        self.check_wrap("abcd efgh", 6, ["  abcd", "  efgh"],
+                        initial_indent="  ", subsequent_indent="  ")
+
+    def test_drop_whitespace__whitespace_line(self):
+        # Check that drop_whitespace drops the whole line if a line consists
+        # only of whitespace.
+        text = "abcd    efgh"
+        self.check_wrap(text, 6, ["abcd", "    ", "efgh"],
+                        drop_whitespace=False)
+        self.check_wrap(text, 6, ["abcd", "efgh"])
+
+    def test_drop_whitespace__false(self):
         # SF patch #1581073
         text = " This is a    sentence with     much whitespace."
         self.check_wrap(text, 10,
@@ -348,6 +376,11 @@
                          "with     ", "much white", "space."],
                         drop_whitespace=False)
 
+    def test_drop_whitespace__false_whitespace_only(self):
+        # Check that a whitespace-only string is not dropped when
+        # drop_whitespace is False.
+        self.check_wrap("  ", 10, ["  "], drop_whitespace=False)
+
     def test_split(self):
         # Ensure that the standard _split() method works as advertised
         # in the comments
@@ -477,6 +510,15 @@
         result = fill(self.text, 40, initial_indent="     ")
         self.check(result, expect)
 
+    def test_initial_indent__empty_string(self):
+        # Check that the empty string is not indented.
+        self.check_wrap("", 10, [], initial_indent="++")
+
+    def test_initial_indent__whitespace_only(self):
+        # Check that a whitespace-only string gets indented (when
+        # drop_whitespace is False).
+        self.check_wrap("   ", 10, ["     "], initial_indent="  ",
+                        drop_whitespace=False)
 
     def test_subsequent_indent(self):
         # Test subsequent_indent parameter