diff --git a/jedi/api/helpers.py b/jedi/api/helpers.py
index 236deb02..9b2f2c07 100644
--- a/jedi/api/helpers.py
+++ b/jedi/api/helpers.py
@@ -330,17 +330,14 @@ def _get_call_signature_details_from_error_node(node, additional_children, posit
 
 def get_call_signature_details(module, position):
     leaf = module.get_leaf_for_position(position, include_prefixes=True)
+    # It's easier to deal with the previous token than the next one in this
+    # case.
     if leaf.start_pos >= position:
         # Whitespace / comments after the leaf count towards the previous leaf.
         leaf = leaf.get_previous_leaf()
         if leaf is None:
             return None
 
-    if leaf == ')':
-        # TODO is this ok?
-        if leaf.end_pos == position:
-            leaf = leaf.get_next_leaf()
-
     # Now that we know where we are in the syntax tree, we start to look at
     # parents for possible function definitions.
     node = leaf.parent
@@ -364,11 +361,17 @@ def get_call_signature_details(module, position):
                     continue
                 additional_children.insert(0, n)
 
+        # Find a valid trailer
         if node.type == 'trailer' and node.children[0] == '(':
-            leaf = node.get_previous_leaf()
-            if leaf is None:
-                return None
-            return CallDetails(node.children[0], node.children, position)
+            # Additionally we have to check that an ending parenthesis isn't
+            # interpreted wrong. There are two cases:
+            # 1. Cursor before paren -> The current signature is good
+            # 2. Cursor after paren -> We need to skip the current signature
+            if not (leaf is node.children[-1] and position >= leaf.end_pos):
+                leaf = node.get_previous_leaf()
+                if leaf is None:
+                    return None
+                return CallDetails(node.children[0], node.children, position)
 
         node = node.parent
 
diff --git a/jedi/inference/base_value.py b/jedi/inference/base_value.py
index 57f74c1a..9c0d77ef 100644
--- a/jedi/inference/base_value.py
+++ b/jedi/inference/base_value.py
@@ -8,7 +8,7 @@ just one.
 """
 from functools import reduce
 from operator import add
-from parso.python.tree import ExprStmt, SyncCompFor, Name
+from parso.python.tree import Name
 
 from jedi import debug
 from jedi._compatibility import zip_longest, unicode
diff --git a/test/test_api/test_call_signatures.py b/test/test_api/test_call_signatures.py
index 1e7bf0ea..ff797452 100644
--- a/test/test_api/test_call_signatures.py
+++ b/test/test_api/test_call_signatures.py
@@ -491,6 +491,13 @@ _calls = [
     (code4, 'i(?b,*r,c', 1),
     (code4, 'i(?*', 0),
     (code4, 'i(?**', (0, 1)),
+
+    # Random
+    (code4, 'i(()', 0),
+    (code4, 'i((),', 1),
+    (code4, 'i([(),', 0),
+    (code4, 'i([(,', 1),
+    (code4, 'i(x,()', 1),
 ]
 
 
@@ -625,3 +632,36 @@ def test_call_magic_method(Script):
     assert [p.name for p in sig.params] == ['self', 'baz']
     sig, = Script(code + 'X().__call__(').call_signatures()
     assert [p.name for p in sig.params] == ['baz']
+
+
+@pytest.mark.parametrize('column', [6, 9])
+def test_cursor_after_signature(Script, column):
+    source = dedent("""
+        def foo(*args):
+            pass
+        foo()  # _
+        """)
+
+    script = Script(source, 4, column)
+
+    assert not script.call_signatures()
+
+
+@pytest.mark.parametrize(
+    'code, line, column, name, index', [
+        ('abs(()\ndef foo(): pass', 1, None, 'abs', 0),
+        ('abs(chr()  \ndef foo(): pass', 1, 10, 'abs', 0),
+        ('abs(chr()\ndef foo(): pass', 1, None, 'abs', 0),
+        ('abs(chr()\ndef foo(): pass', 1, 8, 'chr', 0),
+        ('abs(chr()\ndef foo(): pass', 1, 7, 'abs', 0),
+        ('abs(chr  ( \nclass y: pass', 1, None, 'chr', 0),
+        ('abs(chr  ( \nclass y: pass', 1, 8, 'abs', 0),
+        ('abs(chr  ( \nclass y: pass', 1, 9, 'abs', 0),
+        ('abs(chr  ( \nclass y: pass', 1, 10, 'chr', 0),
+    ]
+)
+def test_base_signatures(Script, code, line, column, name, index):
+    sig, = Script(code, line=line, column=column).call_signatures()
+
+    assert sig.name == name
+    assert sig.index == index