diff --git a/src/Type/Generic/TemplateTypeHelper.php b/src/Type/Generic/TemplateTypeHelper.php
index 6f09c29ccb..48ac6f2159 100644
--- a/src/Type/Generic/TemplateTypeHelper.php
+++ b/src/Type/Generic/TemplateTypeHelper.php
@@ -142,9 +142,7 @@ public static function generalizeInferredTemplateType(TemplateType $templateType
 	{
 		if (!$templateType->getVariance()->covariant()) {
 			$isArrayKey = $templateType->getBound()->describe(VerbosityLevel::precise()) === '(int|string)';
-			if ($type->isScalar()->yes() && $isArrayKey) {
-				$type = $type->generalize(GeneralizePrecision::templateArgument());
-			} elseif ($type->isConstantValue()->yes() && (!$templateType->getBound()->isScalar()->yes() || $isArrayKey)) {
+			if ($type->isConstantValue()->yes() && ($isArrayKey || !$templateType->getBound()->isScalar()->yes())) {
 				$type = $type->generalize(GeneralizePrecision::templateArgument());
 			}
 		}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-12601.php b/tests/PHPStan/Analyser/nsrt/bug-12601.php
new file mode 100644
index 0000000000..5b1bde9f73
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-12601.php
@@ -0,0 +1,54 @@
+<?php // lint >= 8.0
+
+declare(strict_types = 1);
+
+namespace Bug12601;
+
+use ArrayIterator;
+use IteratorAggregate;
+use Traversable;
+use function PHPStan\Testing\assertType;
+
+/** @implements IteratorAggregate<non-empty-string, non-empty-string> */
+class HelloWorld implements IteratorAggregate
+{
+	/** @param array<non-empty-string, non-empty-string> $map */
+	public function __construct(private array $map) {}
+
+	/** @return Traversable<non-empty-string, non-empty-string> */
+	public function getIterator(): Traversable
+	{
+		$iterator = new ArrayIterator($this->map);
+		assertType('ArrayIterator<non-empty-string, non-empty-string>', $iterator);
+		return $iterator;
+	}
+}
+
+class HelloWorld3
+{
+	/** @var ArrayIterator<int, string> */
+	private ArrayIterator $a;
+
+	/** @param list<string> $map */
+	public function __construct(private array $map) {
+		$a = new ArrayIterator($this->map);
+		assertType('ArrayIterator<int<0, max>, string>', $a);
+
+		$this->a = $a;
+	}
+}
+
+/** @implements IteratorAggregate<int<0, max>, non-empty-string> */
+class HelloWorld2 implements IteratorAggregate
+{
+	/** @param array<int<0, max>, non-empty-string> $map */
+	public function __construct(private array $map) {}
+
+	/** @return ArrayIterator<int<0, max>, non-empty-string> */
+	public function getIterator(): Traversable
+	{
+		$iterator = new ArrayIterator($this->map);
+		assertType('ArrayIterator<int<0, max>, non-empty-string>', $iterator);
+		return $iterator;
+	}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/generics-do-not-generalize.php b/tests/PHPStan/Analyser/nsrt/generics-do-not-generalize.php
index d00b8b699a..67b1a40ee8 100644
--- a/tests/PHPStan/Analyser/nsrt/generics-do-not-generalize.php
+++ b/tests/PHPStan/Analyser/nsrt/generics-do-not-generalize.php
@@ -97,7 +97,7 @@ function (): void {
 	/** @var list<string> $a */
 	$a = doFoo();
 
-	assertType('ArrayIterator<int, string>', new ArrayIterator($a));
+	assertType('ArrayIterator<int<0, max>, string>', new ArrayIterator($a));
 };
 
 /**
@@ -115,7 +115,7 @@ function (): void {
 	/** @var list<string> $a */
 	$a = doFoo();
 
-	assertType('ArrayIterator<int, string>', createArrayIterator($a));
+	assertType('ArrayIterator<int<0, max>, string>', createArrayIterator($a));
 };
 
 /** @template T */