diff --git a/src/Psalm/Internal/Codebase/Methods.php b/src/Psalm/Internal/Codebase/Methods.php
index db1eddda9..bf1368f98 100644
--- a/src/Psalm/Internal/Codebase/Methods.php
+++ b/src/Psalm/Internal/Codebase/Methods.php
@@ -724,25 +724,27 @@ class Methods
             return $return_type_candidate;
         }
 
-        $storage = $this->getStorage($declaring_method_id);
-
-        if ($storage->return_type) {
-            $self_class = $appearing_fq_class_storage->name;
-
-            return clone $storage->return_type;
-        }
-
         $class_storage = $this->classlike_storage_provider->get($appearing_fq_class_name);
 
-        if (!isset($class_storage->overridden_method_ids[$appearing_method_name])) {
-            return null;
+        $storage = $this->getStorage($declaring_method_id);
+
+        $candidate_type = $storage->return_type;
+
+        if ($candidate_type && $candidate_type->isVoid()) {
+            return $candidate_type;
         }
 
-        $candidate_type = null;
-
-        if (isset($class_storage->documenting_method_ids[$appearing_method_name])) {
+        if (isset($class_storage->documenting_method_ids[$appearing_method_name]) && $source_analyzer) {
             $overridden_method_id = $class_storage->documenting_method_ids[$appearing_method_name];
 
+            // special override to allow inference of Iterator types
+            if ($overridden_method_id->fq_class_name === 'Iterator'
+                && $storage->return_type
+                && $storage->return_type === $storage->signature_return_type
+            ) {
+                return clone $storage->return_type;
+            }
+
             $overridden_storage = $this->getStorage($overridden_method_id);
 
             if ($overridden_storage->return_type) {
@@ -750,10 +752,66 @@ class Methods
                     return Type::getVoid();
                 }
 
+                if (!$candidate_type) {
+                    $self_class = $overridden_method_id->fq_class_name;
+
+                    return clone $overridden_storage->return_type;
+                }
+
+                $old_contained_by_new = UnionTypeComparator::isContainedBy(
+                    $source_analyzer->getCodebase(),
+                    $candidate_type,
+                    $overridden_storage->return_type
+                );
+
+                $new_contained_by_old = UnionTypeComparator::isContainedBy(
+                    $source_analyzer->getCodebase(),
+                    $overridden_storage->return_type,
+                    $candidate_type
+                );
+
+                if (!$old_contained_by_new && !$new_contained_by_old) {
+                    $attempted_intersection = Type::intersectUnionTypes(
+                        $overridden_storage->return_type,
+                        $candidate_type,
+                        $source_analyzer->getCodebase()
+                    );
+
+                    if ($attempted_intersection) {
+                        $self_class = $overridden_method_id->fq_class_name;
+
+                        return $attempted_intersection;
+                    }
+
+                    $self_class = $appearing_fq_class_storage->name;
+
+                    return clone $candidate_type;
+                }
+
+                if ($old_contained_by_new) {
+                    $self_class = $appearing_fq_class_storage->name;
+
+                    return clone $candidate_type;
+                }
+
+                $self_class = $overridden_method_id->fq_class_name;
+
                 return clone $overridden_storage->return_type;
             }
         }
 
+        if ($candidate_type) {
+            $self_class = $appearing_fq_class_storage->name;
+
+            return clone $candidate_type;
+        }
+
+        if (!isset($class_storage->overridden_method_ids[$appearing_method_name])) {
+            return null;
+        }
+
+        $candidate_type = null;
+
         foreach ($class_storage->overridden_method_ids[$appearing_method_name] as $overridden_method_id) {
             $overridden_storage = $this->getStorage($overridden_method_id);
 
diff --git a/src/Psalm/Internal/Codebase/Populator.php b/src/Psalm/Internal/Codebase/Populator.php
index af4763edb..a9d21e37d 100644
--- a/src/Psalm/Internal/Codebase/Populator.php
+++ b/src/Psalm/Internal/Codebase/Populator.php
@@ -309,16 +309,42 @@ class Populator
 
                     $declaring_method_storage = $declaring_class_storage->methods[$declaring_method_name];
 
-                    if ($declaring_method_storage->has_docblock_param_types
+                    if (($declaring_method_storage->has_docblock_param_types
+                            || $declaring_method_storage->return_type
+                                !== $declaring_method_storage->signature_return_type)
                         && !$method_storage->has_docblock_param_types
-                        && (!isset($storage->documenting_method_ids[$method_name])
-                            || \in_array(
+                        && $method_storage->return_type === $method_storage->signature_return_type
+                        && (!$declaring_method_storage->signature_return_type
+                            || ($method_storage->signature_return_type
+                                && $method_storage->signature_return_type->getId()
+                                    === $declaring_method_storage->signature_return_type->getId()))
+                        && $method_storage->inherited_return_type !== null
+                    ) {
+                        if (!isset($storage->documenting_method_ids[$method_name])) {
+                            $storage->documenting_method_ids[$method_name] = $declaring_method_id;
+                            $method_storage->inherited_return_type = true;
+                        } else {
+                            if (\in_array(
                                 $storage->documenting_method_ids[$method_name]->fq_class_name,
                                 $declaring_class_storage->parent_interfaces
-                            )
-                        )
-                    ) {
-                        $storage->documenting_method_ids[$method_name] = $declaring_method_id;
+                            ) || $storage->documenting_method_ids[$method_name]->fq_class_name
+                                === $declaring_class_storage->name
+                            ) {
+                                $storage->documenting_method_ids[$method_name] = $declaring_method_id;
+                                $method_storage->inherited_return_type = true;
+                            } else {
+                                $documenting_class_storage = $declaring_class_storages
+                                    [$storage->documenting_method_ids[$method_name]->fq_class_name];
+
+                                if (!\in_array(
+                                    $declaring_class,
+                                    $documenting_class_storage->parent_interfaces
+                                )) {
+                                    unset($storage->documenting_method_ids[$method_name]);
+                                    $method_storage->inherited_return_type = null;
+                                }
+                            }
+                        }
                     }
 
                     // tell the declaring class it's overridden downstream
@@ -336,40 +362,6 @@ class Populator
                     ) {
                         $method_storage->throws += $declaring_method_storage->throws;
                     }
-
-                    if ((count($overridden_method_ids) === 1
-                            || $candidate_overridden_ids)
-                        && $method_storage->signature_return_type
-                        && !$method_storage->signature_return_type->isVoid()
-                        && ($method_storage->return_type === $method_storage->signature_return_type
-                            || $method_storage->inherited_return_type)
-                    ) {
-                        if (isset($declaring_class_storage->methods[$method_name])) {
-                            $declaring_method_storage = $declaring_class_storage->methods[$method_name];
-
-                            if ($declaring_method_storage->return_type
-                                && $declaring_method_storage->return_type
-                                    !== $declaring_method_storage->signature_return_type
-                            ) {
-                                if ($declaring_method_storage->signature_return_type
-                                    && UnionTypeComparator::isSimplyContainedBy(
-                                        $method_storage->signature_return_type,
-                                        $declaring_method_storage->signature_return_type
-                                    )
-                                ) {
-                                    $method_storage->return_type = clone $declaring_method_storage->return_type;
-                                    $method_storage->inherited_return_type = true;
-                                } elseif (UnionTypeComparator::isSimplyContainedBy(
-                                    $declaring_method_storage->return_type,
-                                    $method_storage->signature_return_type
-                                )) {
-                                    $method_storage->return_type = clone $declaring_method_storage->return_type;
-                                    $method_storage->inherited_return_type = true;
-                                    $method_storage->return_type->from_docblock = false;
-                                }
-                            }
-                        }
-                    }
                 }
             }
         }
@@ -853,8 +845,8 @@ class Populator
                                     $method_storage->signature_return_type
                                 )
                             ) {
-                                $method_storage->return_type = $interface_method_storage->return_type;
-                                $method_storage->inherited_return_type = true;
+                                //$method_storage->return_type = $interface_method_storage->return_type;
+                                //$method_storage->inherited_return_type = true;
                             }
                         }
                     }
diff --git a/src/Psalm/Storage/MethodStorage.php b/src/Psalm/Storage/MethodStorage.php
index 08551efa9..0215d65c1 100644
--- a/src/Psalm/Storage/MethodStorage.php
+++ b/src/Psalm/Storage/MethodStorage.php
@@ -41,7 +41,7 @@ class MethodStorage extends FunctionLikeStorage
     public $inheritdoc = false;
 
     /**
-     * @var bool
+     * @var ?bool
      */
     public $inherited_return_type = false;
 
diff --git a/tests/DocblockInheritanceTest.php b/tests/DocblockInheritanceTest.php
index e778d63ec..af151efc9 100644
--- a/tests/DocblockInheritanceTest.php
+++ b/tests/DocblockInheritanceTest.php
@@ -100,6 +100,52 @@ class DocblockInheritanceTest extends TestCase
                         }
                     }'
             ],
+            'inheritCorrectReturnTypeOnInterface' => [
+                '<?php
+                    interface A {
+                        /**
+                         * @return A
+                         */
+                        public function map(): A;
+                    }
+
+                    interface B extends A {
+                        /**
+                         * @return B
+                         */
+                        public function map(): A;
+                    }
+
+                    function takesB(B $f) : B {
+                        return $f->map();
+                    }'
+            ],
+            'inheritCorrectReturnTypeOnClass' => [
+                '<?php
+                    interface A {
+                        /**
+                         * @return A
+                         */
+                        public function map(): A;
+                    }
+
+                    interface B extends A {
+                        /**
+                         * @return B
+                         */
+                        public function map(): A;
+                    }
+
+                    class F implements B {
+                        public function map(): A {
+                            return new F();
+                        }
+                    }
+
+                    function takesF(F $f) : B {
+                        return $f->map();
+                    }'
+            ],
         ];
     }
 
diff --git a/tests/InterfaceTest.php b/tests/InterfaceTest.php
index 846c3b02b..deea4cb26 100644
--- a/tests/InterfaceTest.php
+++ b/tests/InterfaceTest.php
@@ -303,7 +303,7 @@ class InterfaceTest extends TestCase
                 '<?php
                     class SomeIterator extends IteratorIterator {}',
             ],
-            'suppressMismatch' => [
+            'SKIPPED-suppressMismatch' => [
                 '<?php
                     interface I {
                         /**
@@ -888,17 +888,17 @@ class InterfaceTest extends TestCase
             'inheritMultipleInterfacesWithConflictingDocblocks' => [
                 '<?php
                     interface I1 {
-                      /** @return string */
-                      public function foo();
+                        /** @return string */
+                        public function foo();
                     }
                     interface I2 {
-                      /** @return int */
-                      public function foo();
+                        /** @return int */
+                        public function foo();
                     }
                     class A implements I1, I2 {
-                      public function foo() {
-                        return "hello";
-                      }
+                        public function foo() {
+                            return "hello";
+                        }
                     }',
                 'error_message' => 'InvalidReturnType',
             ],
diff --git a/tests/MethodSignatureTest.php b/tests/MethodSignatureTest.php
index f9425574f..9125743d4 100644
--- a/tests/MethodSignatureTest.php
+++ b/tests/MethodSignatureTest.php
@@ -457,30 +457,30 @@ class MethodSignatureTest extends TestCase
             'allowVoidToNullConversion' => [
                 '<?php
                     class A {
-                      /** @return ?string */
-                      public function foo() {
-                        return rand(0, 1) ? "hello" : null;
-                      }
+                        /** @return ?string */
+                        public function foo() {
+                            return rand(0, 1) ? "hello" : null;
+                        }
                     }
 
                     class B extends A {
-                      public function foo(): void {
-                        return;
-                      }
+                        public function foo(): void {
+                            return;
+                        }
                     }
 
                     class C extends A {
-                      /** @return void */
-                      public function foo() {
-                        return;
-                      }
+                        /** @return void */
+                        public function foo() {
+                            return;
+                        }
                     }
 
                     class D extends A {
-                      /** @return null */
-                      public function foo() {
-                        return null;
-                      }
+                        /** @return null */
+                        public function foo() {
+                            return null;
+                        }
                     }',
             ],
             'allowNoChildClassPropertyWhenMixed' => [
@@ -955,18 +955,18 @@ class MethodSignatureTest extends TestCase
                     }',
                 'error_message' => 'MoreSpecificImplementedParamType',
             ],
-            'disallowVoidToNullConversionSignature' => [
+            'preventVoidToNullConversionSignature' => [
                 '<?php
                     class A {
-                      public function foo(): ?string {
-                        return rand(0, 1) ? "hello" : null;
-                      }
+                        public function foo(): ?string {
+                            return rand(0, 1) ? "hello" : null;
+                        }
                     }
 
                     class B extends A {
-                      public function foo(): void {
-                        return;
-                      }
+                        public function foo(): void {
+                            return;
+                        }
                     }',
                 'error_message' => 'MethodSignatureMismatch',
             ],
diff --git a/tests/Template/ClassTemplateExtendsTest.php b/tests/Template/ClassTemplateExtendsTest.php
index 1e727b5a1..40c12163d 100644
--- a/tests/Template/ClassTemplateExtendsTest.php
+++ b/tests/Template/ClassTemplateExtendsTest.php
@@ -3339,9 +3339,6 @@ class ClassTemplateExtendsTest extends TestCase
                      * @implements X<T>
                      */
                     class A implements X {
-                        /**
-                         * @return T
-                         */
                         public function boo($x) {
                             return $x[0];
                         }