diff --git a/src/Analyser/Generics/TemplateArgumentSolver.php b/src/Analyser/Generics/TemplateArgumentSolver.php
index 25fcb53900b..df66ea705cb 100644
--- a/src/Analyser/Generics/TemplateArgumentSolver.php
+++ b/src/Analyser/Generics/TemplateArgumentSolver.php
@@ -134,6 +134,9 @@ private function removeSelfBounds(Type $type, string $key): Type
 	/** @var array<string, true> */
 	private array $resolving = [];
 
+	/** How many times a substitution reached a site that was still being resolved. */
+	private int $cyclesReached = 0;
+
 	private function resolveKey(string $key): Type
 	{
 		$key = $this->representative($key);
@@ -144,14 +147,18 @@ private function resolveKey(string $key): Type
 		if (isset($this->resolving[$key])) {
 			// a site whose inferred argument refers back to itself through another
 			// site (wrap($x = new Foo($x))): the inferred type stands
+			$this->cyclesReached++;
 			return $observation['marker']->getDelegate();
 		}
 
 		$this->resolving[$key] = true;
+		$cyclesReached = $this->cyclesReached;
 		try {
 			return $this->resolutions[$key] = $this->resolveObservation($observation);
 		} finally {
 			unset($this->resolving[$key]);
+			// a cycle closed inside another site's resolution was settled there
+			$this->cyclesReached = $cyclesReached;
 		}
 	}
 
@@ -208,7 +215,14 @@ private function resolveObservation(array $observation): Type
 		$template = $observation['marker']->getTemplate();
 		$lowerBounds = [];
 		foreach ($observation['lowerBounds'] as $lowerBound) {
-			$inferred = $template->inferTemplateTypes($this->substituteResolutions($lowerBound))->getType($template->getName());
+			$cyclesReached = $this->cyclesReached;
+			$lowerBound = $this->substituteResolutions($lowerBound);
+			if ($this->cyclesReached !== $cyclesReached) {
+				// the object is sent into its own argument ($map->set($map)): no
+				// finite type contains Foo<itself>, only the bound does
+				return $template->getBound();
+			}
+			$inferred = $template->inferTemplateTypes($lowerBound)->getType($template->getName());
 			if ($inferred === null) {
 				continue;
 			}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-15434.php b/tests/PHPStan/Analyser/nsrt/bug-15434.php
new file mode 100644
index 00000000000..330724c195b
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-15434.php
@@ -0,0 +1,86 @@
+<?php declare(strict_types = 1);
+
+namespace Bug15434Types;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * @template TOwner of object
+ */
+class WeakAnalysingMap
+{
+	/**
+	 * @param TOwner $owner
+	 */
+	public function set(object $owner): void {}
+}
+
+/** @template T */
+class Box
+{
+
+	/** @param T $v */
+	public function add($v): void
+	{
+	}
+
+}
+
+/** @template-contravariant T */
+class Sink
+{
+
+	/** @param T $v */
+	public function put($v): void
+	{
+	}
+
+}
+
+class Test
+{
+
+	public function testSet(): void
+	{
+		$map = new WeakAnalysingMap();
+		assertType('Bug15434Types\WeakAnalysingMap<object>', $map);
+		$map->set($map);
+		assertType('Bug15434Types\WeakAnalysingMap<object>', $map);
+	}
+
+	public function indirectCycle(): void
+	{
+		$a = new WeakAnalysingMap();
+		$b = new WeakAnalysingMap();
+		$a->set($b);
+		$b->set($a);
+		assertType('Bug15434Types\WeakAnalysingMap<Bug15434Types\WeakAnalysingMap<object>>', $a);
+		assertType('Bug15434Types\WeakAnalysingMap<object>', $b);
+	}
+
+	public function afterAnotherLowerBound(): void
+	{
+		$b = new Box();
+		$b->add(1);
+		$b->add($b);
+		assertType('Bug15434Types\Box<mixed>', $b);
+	}
+
+	public function contravariant(): void
+	{
+		$s = new Sink();
+		$s->put($s);
+		assertType('Bug15434Types\Sink<mixed>', $s);
+	}
+
+	public function notACycle(): void
+	{
+		$b = new Box();
+		$c = new Box();
+		$b->add($c);
+		$c->add(1);
+		assertType('Bug15434Types\Box<1>', $c);
+		assertType('Bug15434Types\Box<Bug15434Types\Box<1>>', $b);
+	}
+
+}
diff --git a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
index 8e6c4084026..f754af637bb 100644
--- a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
@@ -4616,4 +4616,12 @@ public function testDeadCatch(): void
 		]);
 	}
 
+	public function testBug15434(): void
+	{
+		$this->checkThisOnly = false;
+		$this->checkNullables = true;
+		$this->checkUnionTypes = true;
+		$this->analyse([__DIR__ . '/data/bug-15434.php'], []);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Methods/data/bug-15434.php b/tests/PHPStan/Rules/Methods/data/bug-15434.php
new file mode 100644
index 00000000000..11752e1643b
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-15434.php
@@ -0,0 +1,82 @@
+<?php declare(strict_types = 1);
+
+namespace Bug15434;
+
+class Test
+{
+    public function testSet(): void
+    {
+        $map = new WeakAnalysingMap();
+        $map->set($map);
+	}
+}
+
+/**
+ * @template TOwner of object
+ */
+class WeakAnalysingMap
+{
+    /**
+     * @param TOwner $owner
+     */
+    public function set(object $owner): void {}
+}
+
+/** @template T */
+class Box
+{
+
+	/** @param T $v */
+	public function __construct($v = null)
+	{
+	}
+
+	/** @param T $v */
+	public function add($v): void
+	{
+	}
+
+	/** @param list<T> $v */
+	public function addAll(array $v): void
+	{
+	}
+
+}
+
+class Analogous
+{
+
+	public function indirectCycle(): void
+	{
+		$a = new WeakAnalysingMap();
+		$b = new WeakAnalysingMap();
+		$a->set($b);
+		$b->set($a);
+	}
+
+	public function afterAnotherLowerBound(): void
+	{
+		$b = new Box();
+		$b->add(1);
+		$b->add($b);
+	}
+
+	public function wrappedInList(): void
+	{
+		$b = new Box();
+		$b->addAll([$b]);
+	}
+
+	public function wrappedInArray(): void
+	{
+		$b = new Box();
+		$b->add([$b]);
+	}
+
+	public function withInitialType(): void
+	{
+		$b = new Box(1);
+		$b->add($b);
+	}
+
+}