diff --git a/Lib/codecs.py b/Lib/codecs.py
index 590238ec502..e120d636bcb 100644
--- a/Lib/codecs.py
+++ b/Lib/codecs.py
@@ -472,15 +472,17 @@ class StreamReader(Codec):
             self.charbuffer = "".join(self.linebuffer)
             self.linebuffer = None
 
+        if chars < 0:
+            # For compatibility with other read() methods that take a
+            # single argument
+            chars = size
+
         # read until we get the required number of characters (if available)
         while True:
             # can the request be satisfied from the character buffer?
             if chars >= 0:
                 if len(self.charbuffer) >= chars:
                     break
-            elif size >= 0:
-                if len(self.charbuffer) >= size:
-                    break
             # we need more data
             if size < 0:
                 newdata = self.stream.read()
diff --git a/Lib/test/test_codecs.py b/Lib/test/test_codecs.py
index efc40cf2c23..0ec8bf5a4b4 100644
--- a/Lib/test/test_codecs.py
+++ b/Lib/test/test_codecs.py
@@ -149,19 +149,33 @@ class ReadTest(unittest.TestCase):
         self.assertEqual(f.read(), ''.join(lines[1:]))
         self.assertEqual(f.read(), '')
 
+        # Issue #32110: Test readline() followed by read(n)
+        f = getreader()
+        self.assertEqual(f.readline(), lines[0])
+        self.assertEqual(f.read(1), lines[1][0])
+        self.assertEqual(f.read(0), '')
+        self.assertEqual(f.read(100), data[len(lines[0]) + 1:][:100])
+
         # Issue #16636: Test readline() followed by readlines()
         f = getreader()
         self.assertEqual(f.readline(), lines[0])
         self.assertEqual(f.readlines(), lines[1:])
         self.assertEqual(f.read(), '')
 
-        # Test read() followed by read()
+        # Test read(n) followed by read()
         f = getreader()
         self.assertEqual(f.read(size=40, chars=5), data[:5])
         self.assertEqual(f.read(), data[5:])
         self.assertEqual(f.read(), '')
 
-        # Issue #12446: Test read() followed by readlines()
+        # Issue #32110: Test read(n) followed by read(n)
+        f = getreader()
+        self.assertEqual(f.read(size=40, chars=5), data[:5])
+        self.assertEqual(f.read(1), data[5])
+        self.assertEqual(f.read(0), '')
+        self.assertEqual(f.read(100), data[6:106])
+
+        # Issue #12446: Test read(n) followed by readlines()
         f = getreader()
         self.assertEqual(f.read(size=40, chars=5), data[:5])
         self.assertEqual(f.readlines(), [lines[0][5:]] + lines[1:])
diff --git a/Misc/NEWS.d/next/Library/2017-11-22-09-44-15.bpo-32110.VJa9bo.rst b/Misc/NEWS.d/next/Library/2017-11-22-09-44-15.bpo-32110.VJa9bo.rst
new file mode 100644
index 00000000000..b57ff1acaff
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2017-11-22-09-44-15.bpo-32110.VJa9bo.rst
@@ -0,0 +1,3 @@
+``codecs.StreamReader.read(n)`` now returns not more than *n*
+characters/bytes for non-negative *n*. This makes it compatible with
+``read()`` methods of other file-like objects.