diff --git a/docs/collection/api/collection.md b/docs/collection/api/collection.md
index 018391f..00bed89 100644
--- a/docs/collection/api/collection.md
+++ b/docs/collection/api/collection.md
@@ -333,19 +333,19 @@ groupBy(Closure $keySelector, ?Closure $valueTransform = null): Map<K, Collectio
 Group elements by key selector `(E, int): K`. When a `$valueTransform` `(E, int): V` is provided, each element is transformed before being added to its group — the result is `Map<K, ImmutableList<V>>`.
 
 ```php
-intersect(iterable $other): ImmutableSet<E>
+intersect(iterable<V> $other): ImmutableSet<E&V>
 ```
-Elements present in both this collection and the iterable. Returns a set (duplicates removed).
+Elements present in both this collection and the iterable. Returns a set (duplicates removed). The element type narrows to `E&V` — only values that can belong to both sides.
 
 ```php
-union(iterable $other): ImmutableSet<E>
+union(iterable<NE> $other): ImmutableSet<E|NE>
 ```
-All elements from both this collection and the iterable. Returns a set (duplicates removed).
+All elements from both this collection and the iterable. Returns a set (duplicates removed). The element type widens to `E|NE`, like `add()`.
 
 ```php
-subtract(iterable $other): ImmutableSet<E>
+subtract(iterable<mixed> $other): ImmutableSet<E>
 ```
-Elements present in this collection but not in the iterable. Returns a set (duplicates removed).
+Elements present in this collection but not in the iterable. Returns a set (duplicates removed). The element type is always `E` — any iterable may be subtracted.
 
 ## Ordering
 
diff --git a/src/Collection.php b/src/Collection.php
index 216bb3f..4f2f0b3 100644
--- a/src/Collection.php
+++ b/src/Collection.php
@@ -582,8 +582,9 @@ public function groupBy(Closure $keySelector, ?Closure $valueTransform = null):
 	/**
 	 * Returns a set containing only elements present in both this collection and the given iterable.
 	 *
-	 * @param iterable<E> $other
-	 * @return Set<E>
+	 * @template V
+	 * @param iterable<V> $other
+	 * @return Set<E&V>
 	 */
 	#[NoDiscard]
 	public function intersect(iterable $other): Set;
@@ -591,8 +592,9 @@ public function intersect(iterable $other): Set;
 	/**
 	 * Returns a set containing all elements from both this collection and the given iterable.
 	 *
-	 * @param iterable<E> $other
-	 * @return Set<E>
+	 * @template NE
+	 * @param iterable<NE> $other
+	 * @return Set<E|NE>
 	 */
 	#[NoDiscard]
 	public function union(iterable $other): Set;
@@ -600,7 +602,7 @@ public function union(iterable $other): Set;
 	/**
 	 * Returns a set containing elements present in this collection but not in the given iterable.
 	 *
-	 * @param iterable<E> $other
+	 * @param iterable<mixed> $other
 	 * @return Set<E>
 	 */
 	#[NoDiscard]
diff --git a/src/CollectionLogic.php b/src/CollectionLogic.php
index 1368fbd..b83ffe3 100644
--- a/src/CollectionLogic.php
+++ b/src/CollectionLogic.php
@@ -957,7 +957,9 @@ public function groupBy(Closure $keySelector, ?Closure $valueTransform = null):
 	/**
 	 * {@inheritDoc}
 	 *
-	 * @return ImmutableSet<E>
+	 * @template U
+	 * @param iterable<U> $other
+	 * @return ImmutableSet<E&U>
 	 */
 	#[NoDiscard]
 	public function intersect(iterable $other): ImmutableSet
@@ -968,7 +970,9 @@ public function intersect(iterable $other): ImmutableSet
 	/**
 	 * {@inheritDoc}
 	 *
-	 * @return ImmutableSet<E>
+	 * @template NE
+	 * @param iterable<NE> $other
+	 * @return ImmutableSet<E|NE>
 	 */
 	#[NoDiscard]
 	public function union(iterable $other): ImmutableSet
@@ -979,6 +983,7 @@ public function union(iterable $other): ImmutableSet
 	/**
 	 * {@inheritDoc}
 	 *
+	 * @param iterable<mixed> $other
 	 * @return ImmutableSet<E>
 	 */
 	#[NoDiscard]
diff --git a/src/Operation/SetOperation.php b/src/Operation/SetOperation.php
index 664c605..059d979 100644
--- a/src/Operation/SetOperation.php
+++ b/src/Operation/SetOperation.php
@@ -20,8 +20,9 @@
 final class SetOperation extends AbstractOperation
 {
 	/**
-	 * @param iterable<V> $other
-	 * @return Generator<V>
+	 * @template U
+	 * @param iterable<U> $other
+	 * @return Generator<V&U>
 	 */
 	public function intersect(iterable $other): Generator
 	{
@@ -35,14 +36,16 @@ public function intersect(iterable $other): Generator
 			$hash = KeyHasher::hashSetKey($v);
 			if (isset($otherSet[$hash]) && !isset($seen[$hash])) {
 				$seen[$hash] = true;
-				yield $v;
+				// Hash membership in $otherSet means the value also occurs in $other.
+				yield $v; // @phpstan-ignore generator.valueType
 			}
 		}
 	}
 
 	/**
-	 * @param iterable<V> $other
-	 * @return Generator<V>
+	 * @template U
+	 * @param iterable<U> $other
+	 * @return Generator<V|U>
 	 */
 	public function union(iterable $other): Generator
 	{
@@ -65,7 +68,7 @@ public function union(iterable $other): Generator
 	}
 
 	/**
-	 * @param iterable<V> $other
+	 * @param iterable<mixed> $other
 	 * @return Generator<V>
 	 */
 	public function subtract(iterable $other): Generator
diff --git a/src/Set/SelfPreservingImmutableSetLogic.php b/src/Set/SelfPreservingImmutableSetLogic.php
index 81da310..7bf0dcd 100644
--- a/src/Set/SelfPreservingImmutableSetLogic.php
+++ b/src/Set/SelfPreservingImmutableSetLogic.php
@@ -36,9 +36,11 @@
  * `newCollectionOf()` builds derived collections with `new static(...)`, so there is
  * no factory method to override.
  *
- * Two consequences of the `static` promise, both intentional:
+ * Three consequences of the `static` promise, all intentional:
  * - Mutations are **strict**: unlike the widening base `add(NE): ImmutableSet<E|NE>`,
  *   here `add(E): static`. A fixed-type collection cannot widen its element type.
+ * - `union()` is **strict** for the same reason: unlike the widening base
+ *   `union(iterable<NE>): Set<E|NE>`, here `union(iterable<E>): static`.
  * - Type-changing methods (map, flatMap, flatten, filterInstanceOf, groupBy, the
  *   to* conversions) are **not** narrowed — they still return the base type, because
  *   their result is no longer a collection of `E`. (`groupBy` additionally cannot be
@@ -424,7 +426,8 @@ public function shuffled(): static
 	/**
 	 * {@inheritDoc}
 	 *
-	 * @param iterable<E> $other
+	 * @template V
+	 * @param iterable<V> $other
 	 * @return static
 	 */
 	#[NoDiscard]
@@ -448,7 +451,7 @@ public function union(iterable $other): static
 	/**
 	 * {@inheritDoc}
 	 *
-	 * @param iterable<E> $other
+	 * @param iterable<mixed> $other
 	 * @return static
 	 */
 	#[NoDiscard]
diff --git a/src/Set/SetLogic.php b/src/Set/SetLogic.php
index 041409e..c964bbc 100644
--- a/src/Set/SetLogic.php
+++ b/src/Set/SetLogic.php
@@ -376,7 +376,9 @@ public function groupBy(Closure $keySelector, ?Closure $valueTransform = null):
 	 * Routed through newCollectionOf (rather than the free setOf) so that subtypes
 	 * which override the factory preserve their own type. Defaults to ImmutableSet.
 	 *
-	 * @return ImmutableSet<E>
+	 * @template U
+	 * @param iterable<U> $other
+	 * @return ImmutableSet<E&U>
 	 */
 	#[NoDiscard]
 	public function intersect(iterable $other): ImmutableSet
@@ -387,7 +389,9 @@ public function intersect(iterable $other): ImmutableSet
 	/**
 	 * {@inheritDoc}
 	 *
-	 * @return ImmutableSet<E>
+	 * @template NE
+	 * @param iterable<NE> $other
+	 * @return ImmutableSet<E|NE>
 	 */
 	#[NoDiscard]
 	public function union(iterable $other): ImmutableSet
@@ -398,6 +402,7 @@ public function union(iterable $other): ImmutableSet
 	/**
 	 * {@inheritDoc}
 	 *
+	 * @param iterable<mixed> $other
 	 * @return ImmutableSet<E>
 	 */
 	#[NoDiscard]
diff --git a/tests/Type/SetOperationsTypeTest.php b/tests/Type/SetOperationsTypeTest.php
new file mode 100644
index 0000000..d98ae18
--- /dev/null
+++ b/tests/Type/SetOperationsTypeTest.php
@@ -0,0 +1,51 @@
+<?php
+
+/**
+ * This file is part of the Noctud Collection.
+ * Copyright (c) Noctud.dev
+ */
+
+declare(strict_types=1);
+
+namespace Noctud\Collection\Tests\Type;
+
+use Noctud\Collection\Collection;
+use function Noctud\Collection\listOf;
+use function Noctud\Collection\setOf;
+use function PHPStan\Testing\assertType;
+
+/** @var Collection<string> $c */
+$c = listOf(['a', 'b', 'c']);
+/** @var Collection<int|string> $scalars */
+$scalars = listOf([1, 'a']);
+/** @var iterable<int> $ints */
+$ints = [1, 2];
+/** @var iterable<mixed> $anything */
+$anything = [1, 'a'];
+
+// With a same-typed iterable, the element type is unchanged.
+assertType('Noctud\Collection\Set\Set<string>', $c->intersect(['a', 'b']));
+assertType('Noctud\Collection\Set\Set<string>', $c->union(['a', 'b']));
+assertType('Noctud\Collection\Set\Set<string>', $c->subtract(['a', 'b']));
+
+// intersect narrows to E&V: only values that can belong to both sides.
+assertType('Noctud\Collection\Set\Set<int>', $scalars->intersect($ints));
+assertType('Noctud\Collection\Set\Set<string>', $c->intersect($anything));
+// Intersecting disjoint types is reported as an unresolvable return type.
+assertType('Noctud\Collection\Set\Set<*NEVER*>', $c->intersect($ints)); // @phpstan-ignore method.unresolvableReturnType
+
+// union widens to E|V: elements of both sides end up in the result.
+assertType('Noctud\Collection\Set\Set<int|string>', $c->union($ints));
+assertType('Noctud\Collection\Set\Set<int|string>', $scalars->union($ints));
+
+// subtract always keeps E: any iterable may be subtracted.
+assertType('Noctud\Collection\Set\Set<int|string>', $scalars->subtract($ints));
+assertType('Noctud\Collection\Set\Set<string>', $c->subtract($anything));
+
+// Same behavior on a Set receiver.
+$imm = setOf([1, 2, 3]);
+/** @var iterable<string> $strings */
+$strings = ['a', 'b'];
+assertType('Noctud\Collection\Set\Set<*NEVER*>', $imm->intersect($strings)); // @phpstan-ignore method.unresolvableReturnType
+assertType('Noctud\Collection\Set\Set<int|string>', $imm->union($strings));
+assertType('Noctud\Collection\Set\Set<int>', $imm->subtract($strings));