diff --git a/jedi/api/completion.py b/jedi/api/completion.py
index a2ac4d04..342f7506 100644
--- a/jedi/api/completion.py
+++ b/jedi/api/completion.py
@@ -195,7 +195,6 @@ class Completion:
         - In args: */**: no completion
         - In params (also lambda): no completion before =
         """
-
         grammar = self._inference_state.grammar
         self.stack = stack = None
         self._position = (
@@ -278,6 +277,10 @@ class Completion:
                 )
             elif nonterminals[-1] in ('trailer', 'dotted_name') and nodes[-1] == '.':
                 dot = self._module_node.get_leaf_for_position(self._position)
+                if dot.type == "endmarker":
+                    # This is a bit of a weird edge case, maybe we can somehow
+                    # generalize this.
+                    dot = leaf.get_previous_leaf()
                 cached_name, n = self._complete_trailer(dot.get_previous_leaf())
                 completion_names += n
             elif self._is_parameter_completion():
diff --git a/test/completion/docstring.py b/test/completion/docstring.py
index 5160610f..b2d02239 100644
--- a/test/completion/docstring.py
+++ b/test/completion/docstring.py
@@ -284,6 +284,13 @@ def doctest_with_space():
         import_issu
     """
 
+def doctest_issue_github_1748():
+    """From GitHub #1748
+    #? 10 []
+    This. Al
+    """
+    pass
+
 
 def docstring_rst_identifiers():
     """
diff --git a/test/test_api/test_completion.py b/test/test_api/test_completion.py
index 8e5ec3b2..de46223e 100644
--- a/test/test_api/test_completion.py
+++ b/test/test_api/test_completion.py
@@ -457,3 +457,7 @@ def test_module_completions(Script, module):
         # Just make sure that there are no errors
         c.type
         c.docstring()
+
+
+def test_whitespace_at_end_after_dot(Script):
+    assert 'strip' in [c.name for c in Script('str. ').complete()]