diff --git a/Lib/inspect.py b/Lib/inspect.py
--- a/Lib/inspect.py
+++ b/Lib/inspect.py
@@ -1572,13 +1572,19 @@
                           _partial_kwarg=_partial_kwarg)
 
     def __str__(self):
+        return self.render()
+
+    def render(self,
+            formatvalue=lambda value: '=' +repr(value),
+            formatpositional=lambda value: '<{}>'.format(value),
+            formatannotation=formatannotation):
         kind = self.kind
 
         formatted = self._name
         if kind == _POSITIONAL_ONLY:
             if formatted is None:
                 formatted = ''
-            formatted = '<{}>'.format(formatted)
+            formatted = formatpositional(formatted)
 
         # Add annotation and default value
         if self._annotation is not _empty:
@@ -1586,7 +1592,7 @@
                                        formatannotation(self._annotation))
 
         if self._default is not _empty:
-            formatted = '{}={}'.format(formatted, repr(self._default))
+            formatted = '{}{}'.format(formatted, formatvalue(self._default))
 
         if kind == _VAR_POSITIONAL:
             formatted = '*' + formatted
@@ -2043,10 +2049,18 @@
         return __bind_self._bind(args, kwargs, partial=True)
 
     def __str__(self):
+        return self.render()
+
+    def render(self,
+            formatvalue=lambda value:'=' + str(value),
+            formatannotation=formatannotation,
+            formatpositional=lambda value: '<{}>'.format(value),
+            islambda=False):
+
         result = []
         render_kw_only_separator = True
         for idx, param in enumerate(self.parameters.values()):
-            formatted = str(param)
+            formatted = param.render(formatvalue, formatpositional, formatannotation)
 
             kind = param.kind
             if kind == _VAR_POSITIONAL:
@@ -2070,4 +2084,7 @@
             anno = formatannotation(self.return_annotation)
             rendered += ' -> {}'.format(anno)
 
+        elif islambda:
+            rendered = rendered[1:-1]
+
         return rendered
diff --git a/Lib/pydoc.py b/Lib/pydoc.py
--- a/Lib/pydoc.py
+++ b/Lib/pydoc.py
@@ -913,21 +913,18 @@
                 reallink = realname
             title = '<a name="%s"><strong>%s</strong></a> = %s' % (
                 anchor, name, reallink)
-        if inspect.isfunction(object):
-            args, varargs, kwonlyargs, kwdefaults, varkw, defaults, ann = \
-                inspect.getfullargspec(object)
-            argspec = inspect.formatargspec(
-                args, varargs, kwonlyargs, kwdefaults, varkw, defaults, ann,
-                formatvalue=self.formatvalue,
-                formatannotation=inspect.formatannotationrelativeto(object))
-            if realname == '<lambda>':
-                title = '<strong>%s</strong> <em>lambda</em> ' % name
-                # XXX lambda's won't usually have func_annotations['return']
-                # since the syntax doesn't support but it is possible.
-                # So removing parentheses isn't truly safe.
-                argspec = argspec[1:-1] # remove parentheses
-        else:
-            argspec = '(...)'
+
+        try:
+            signature = inspect.signature(object)
+        except ValueError:
+            signature = '(...)'
+        argspec = signature.render(formatvalue=self.formatvalue,
+                formatannotation=inspect.formatannotationrelativeto(object),
+                formatpositional=lambda nm: '&lt;{}&gt;'.format(nm),
+                islambda=(inspect.isfunction(object) and realname == '<lambda>'))
+        if inspect.isfunction(object) and realname == '<lambda>':
+            title = '<strong>%s</strong> <em>lambda</em> ' % name
+
 
         decl = title + argspec + (note and self.grey(
                '<font face="helvetica, arial">%s</font>' % note))
@@ -1309,21 +1306,18 @@
                 cl.__dict__[realname] is object):
                 skipdocs = 1
             title = self.bold(name) + ' = ' + realname
-        if inspect.isfunction(object):
-            args, varargs, varkw, defaults, kwonlyargs, kwdefaults, ann = \
-              inspect.getfullargspec(object)
-            argspec = inspect.formatargspec(
-                args, varargs, varkw, defaults, kwonlyargs, kwdefaults, ann,
-                formatvalue=self.formatvalue,
-                formatannotation=inspect.formatannotationrelativeto(object))
-            if realname == '<lambda>':
-                title = self.bold(name) + ' lambda '
-                # XXX lambda's won't usually have func_annotations['return']
-                # since the syntax doesn't support but it is possible.
-                # So removing parentheses isn't truly safe.
-                argspec = argspec[1:-1] # remove parentheses
-        else:
+
+        try:
+            signature = inspect.signature(object)
+            argspec = signature.render(formatvalue=self.formatvalue,
+                formatannotation=inspect.formatannotationrelativeto(object),
+                islambda=(inspect.isfunction(object) and realname == '<lambda>'))
+        except ValueError:
             argspec = '(...)'
+        if inspect.isfunction(object) and realname == '<lambda>':
+            title = title + ' '
+
+
         decl = title + argspec + note
 
         if skipdocs:
diff --git a/Lib/test/test_pydoc.py b/Lib/test/test_pydoc.py
--- a/Lib/test/test_pydoc.py
+++ b/Lib/test/test_pydoc.py
@@ -395,6 +395,36 @@
             synopsis = pydoc.synopsis(TESTFN, {})
             self.assertEqual(synopsis, 'line 1: h\xe9')
 
+    @unittest.skipIf(sys.flags.optimize >= 2,
+                     "Docstrings are omitted with -O2 and above")
+    def test_function_like_signature(self):
+        class Function:
+            def __init__(self):
+                self._func = lambda a=3, b=4: a*b
+
+            def __call__(self, *args, **kwds):
+                return self._func(*args, **kwds)
+
+            @property
+            def __name__(self):
+                return '$function$'
+
+            @property
+            def __signature__(self):
+                return inspect.signature(self._func)
+
+            def __get__(self, a, b):
+                return self
+
+        function = Function()
+        self.assertEqual(function(), 12)
+
+        doc = pydoc.TextDoc()
+        result = doc.document(function)
+
+        self.maxDiff = None
+        self.assertEqual(result, '''$\x08$f\x08fu\x08un\x08nc\x08ct\x08ti\x08io\x08on\x08n$\x08$(a=3, b=4)\n''')
+
 
 class PydocImportTest(unittest.TestCase):