diff --git a/src/Type/Generic/TemplateTypeArgumentStrategy.php b/src/Type/Generic/TemplateTypeArgumentStrategy.php
index ec7541a6c76..025762fe423 100644
--- a/src/Type/Generic/TemplateTypeArgumentStrategy.php
+++ b/src/Type/Generic/TemplateTypeArgumentStrategy.php
@@ -25,8 +25,14 @@ public function accepts(TemplateType $left, Type $right, bool $strictTypes): Tri
 			return TrinaryLogic::createNo();
 		}
 
-		return $left->isSuperTypeOf($right)
-			->or(TrinaryLogic::createFromBoolean($right->equals(new MixedType())));
+		if ($right instanceof TemplateType) {
+			$accepts = $right->isAcceptedBy($left, $strictTypes);
+		} else {
+			$accepts = $left->getBound()->accepts($right, $strictTypes)
+				->and(TrinaryLogic::createMaybe());
+		}
+
+		return $accepts->or(TrinaryLogic::createFromBoolean($right->equals(new MixedType())));
 	}
 
 	public function isArgument(): bool
diff --git a/src/Type/Generic/TemplateTypeTrait.php b/src/Type/Generic/TemplateTypeTrait.php
index 6c6afcc9e7c..5a981128752 100644
--- a/src/Type/Generic/TemplateTypeTrait.php
+++ b/src/Type/Generic/TemplateTypeTrait.php
@@ -112,7 +112,16 @@ public function equals(Type $type): bool
 
 	public function isAcceptedBy(Type $acceptingType, bool $strictTypes): TrinaryLogic
 	{
-		return $this->isSubTypeOf($acceptingType);
+		if (!$acceptingType instanceof TemplateType) {
+			return $acceptingType->accepts($this->getBound(), $strictTypes);
+		}
+
+		if ($this->getScope()->equals($acceptingType->getScope()) && $this->getName() === $acceptingType->getName()) {
+			return $acceptingType->getBound()->accepts($this->getBound(), $strictTypes);
+		}
+
+		return $acceptingType->getBound()->accepts($this->getBound(), $strictTypes)
+			->and(TrinaryLogic::createMaybe());
 	}
 
 	public function accepts(Type $type, bool $strictTypes): TrinaryLogic
diff --git a/tests/PHPStan/Rules/Methods/ReturnTypeRuleTest.php b/tests/PHPStan/Rules/Methods/ReturnTypeRuleTest.php
index 3f9b8ea5d35..b99b23ba491 100644
--- a/tests/PHPStan/Rules/Methods/ReturnTypeRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/ReturnTypeRuleTest.php
@@ -16,9 +16,11 @@ class ReturnTypeRuleTest extends RuleTestCase
 
 	private bool $checkExplicitMixed = false;
 
+	private bool $checkUnionTypes = true;
+
 	protected function getRule(): Rule
 	{
-		return new ReturnTypeRule(new FunctionReturnTypeCheck(new RuleLevelHelper($this->createReflectionProvider(), true, false, true, $this->checkExplicitMixed)));
+		return new ReturnTypeRule(new FunctionReturnTypeCheck(new RuleLevelHelper($this->createReflectionProvider(), true, false, $this->checkUnionTypes, $this->checkExplicitMixed)));
 	}
 
 	public function testReturnTypeRule(): void
@@ -586,4 +588,19 @@ public function testBug6438(): void
 		$this->analyse([__DIR__ . '/data/bug-6438.php'], []);
 	}
 
+	public function testBug6589(): void
+	{
+		$this->checkUnionTypes = false;
+		$this->analyse([__DIR__ . '/data/bug-6589.php'], [
+			[
+				'Method Bug6589\HelloWorldTemplated::getField() should return TField of Bug6589\Field2 but returns Bug6589\Field.',
+				17,
+			],
+			[
+				'Method Bug6589\HelloWorldSimple::getField() should return Bug6589\Field2 but returns Bug6589\Field.',
+				31,
+			],
+		]);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Methods/data/bug-6589.php b/tests/PHPStan/Rules/Methods/data/bug-6589.php
new file mode 100644
index 00000000000..6eb08dda4e3
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-6589.php
@@ -0,0 +1,33 @@
+<?php declare(strict_types = 1);
+
+namespace Bug6589;
+
+class Field {}
+
+class Field2 extends Field {}
+
+/**
+ * @template TField of Field2
+ */
+class HelloWorldTemplated
+{
+	/** @return TField */
+	public function getField()
+	{
+		return new Field();
+	}
+
+	/** @return TField */
+	public function getField2()
+	{
+		return new Field2();
+	}
+}
+
+class HelloWorldSimple
+{
+    public function getField(string $name): Field2
+    {
+        return new Field();
+    }
+}
diff --git a/tests/PHPStan/Type/ObjectTypeTest.php b/tests/PHPStan/Type/ObjectTypeTest.php
index 035fc3ef97c..81298886b5b 100644
--- a/tests/PHPStan/Type/ObjectTypeTest.php
+++ b/tests/PHPStan/Type/ObjectTypeTest.php
@@ -412,7 +412,7 @@ public function dataAccepts(): array
 					new ObjectType(DateTimeInterface::class),
 					TemplateTypeVariance::createInvariant(),
 				),
-				TrinaryLogic::createMaybe(),
+				TrinaryLogic::createNo(),
 			],
 		];
 	}
diff --git a/tests/PHPStan/Type/TemplateTypeTest.php b/tests/PHPStan/Type/TemplateTypeTest.php
index ac4c1ee701e..b3fb3990393 100644
--- a/tests/PHPStan/Type/TemplateTypeTest.php
+++ b/tests/PHPStan/Type/TemplateTypeTest.php
@@ -85,6 +85,12 @@ public function dataAccepts(): array
 				TrinaryLogic::createYes(),
 				TrinaryLogic::createYes(),
 			],
+			'does not accept ObjectType that is a super type of bound' => [
+				$templateType('T', new ObjectType(Iterable::class)),
+				new ObjectType(Traversable::class),
+				TrinaryLogic::createNo(),
+				TrinaryLogic::createNo(),
+			],
 		];
 	}
 
diff --git a/tests/PHPStan/Type/UnionTypeTest.php b/tests/PHPStan/Type/UnionTypeTest.php
index c324442fd80..1a82c405f00 100644
--- a/tests/PHPStan/Type/UnionTypeTest.php
+++ b/tests/PHPStan/Type/UnionTypeTest.php
@@ -919,7 +919,7 @@ public function dataAccepts(): array
 				),
 				TrinaryLogic::createYes(),
 			],
-			'maybe accepts template-of-union sub type of a union member' => [
+			'accepts template-of-union sub type of a union member' => [
 				new UnionType([
 					TemplateTypeFactory::create(
 						TemplateTypeScope::createWithClass('Foo'),
@@ -941,6 +941,30 @@ public function dataAccepts(): array
 					]),
 					TemplateTypeVariance::createInvariant(),
 				),
+				TrinaryLogic::createYes(),
+			],
+			'maybe accepts template-of-union sub type of a union member (argument)' => [
+				new UnionType([
+					TemplateTypeFactory::create(
+						TemplateTypeScope::createWithClass('Foo'),
+						'T',
+						new UnionType([
+							new IntegerType(),
+							new FloatType(),
+						]),
+						TemplateTypeVariance::createInvariant(),
+					)->toArgument(),
+					new NullType(),
+				]),
+				TemplateTypeFactory::create(
+					TemplateTypeScope::createWithClass('Bar'),
+					'T',
+					new UnionType([
+						new IntegerType(),
+						new FloatType(),
+					]),
+					TemplateTypeVariance::createInvariant(),
+				),
 				TrinaryLogic::createMaybe(),
 			],
 			'accepts template-of-string equal to a union member' => [