diff --git a/jedi/api/completion.py b/jedi/api/completion.py
index e28559fd..1b43657b 100644
--- a/jedi/api/completion.py
+++ b/jedi/api/completion.py
@@ -18,6 +18,7 @@ from jedi.inference.context import get_global_filters
 from jedi.inference.value import TreeInstance
 from jedi.inference.gradual.conversion import convert_values
 from jedi.parser_utils import cut_value_at_position
+from jedi.plugins import plugin_manager
 
 
 def get_signature_param_names(signatures):
@@ -74,6 +75,13 @@ def get_flow_scope_node(module_node, position):
     return node
 
 
+@plugin_manager.decorate()
+def complete_param_names(context, function_name):
+    # Basically there's no way to do param completion. The plugins are
+    # responsible for this.
+    return []
+
+
 class Completion:
     def __init__(self, inference_state, module_context, code_lines, position,
                  signatures_callback, fuzzy=False):
@@ -217,7 +225,14 @@ class Completion:
                 dot = self._module_node.get_leaf_for_position(self._position)
                 completion_names += self._complete_trailer(dot.get_previous_leaf())
             elif self._is_parameter_completion():
-                pass
+                stack_node = self.stack[-2]
+                if stack_node.nonterminal == 'parameters':
+                    stack_node = self.stack[-3]
+                if stack_node.nonterminal == 'funcdef':
+                    context = get_user_context(self._module_context, self._position)
+                    function_name = stack_node.nodes[1]
+
+                    completion_names += complete_param_names(context, function_name)
             else:
                 completion_names += self._complete_global_scope()
                 completion_names += self._complete_inherited(is_function=False)
diff --git a/jedi/plugins/pytest.py b/jedi/plugins/pytest.py
index 8cdfb609..b4e6d579 100644
--- a/jedi/plugins/pytest.py
+++ b/jedi/plugins/pytest.py
@@ -53,6 +53,18 @@ def goto_anonymous_param(func):
     return wrapper
 
 
+def complete_param_names(func):
+    def wrapper(context, func_name):
+        module_context = context.get_root_context()
+        names = []
+        for module_context in _iter_pytest_modules(module_context):
+            names += FixtureFilter(module_context).values()
+        if names:
+            return names
+        return func(context, func_name)
+    return wrapper
+
+
 def _goto_pytest_fixture(module_context, name):
     for module_context in _iter_pytest_modules(module_context):
         names = FixtureFilter(module_context).get(name)
diff --git a/test/completion/pytest.py b/test/completion/pytest.py
index b8423c16..b6f8adca 100644
--- a/test/completion/pytest.py
+++ b/test/completion/pytest.py
@@ -54,9 +54,21 @@ def test_x(MyClassFixture):
 #? 34 ['my_fixture']
 def test_x(my_simple_fixture, my_fixture):
     return
+#? 34 ['my_fixture']
+def test_x(my_simple_fixture, my_fixture):
+    return
+#? ['my_fixture']
+def test_x(my_simple_fixture, my_f
+    return
 #? 18 ['my_simple_fixture']
 def test_x(my_simple_fixture):
     return
+#? ['my_simple_fixture']
+def test_x(my_simp
+    return
+#? ['my_conftest_fixture']
+def test_x(my_con
+    return
 #? 18 ['my_conftest_fixture']
 def test_x(my_conftest_fixture):
     return