diff --git a/README.md b/README.md
index e0bf45e..874a1bc 100644
--- a/README.md
+++ b/README.md
@@ -268,6 +268,9 @@ A few consequences worth knowing:
 - `merge()` merges arrays and `Ds\Map` by key (integer keys of arrays are kept, unlike `array_merge()`); for other
   inputs it appends.
 - `sort()`/`sortBy()` are stable and never modify their input, unlike `Ds\Seq::sort()`.
+- `sort()` without a comparator and `sortBy()` sort natively, comparing like `<=>`. The one difference is enums,
+  which `<=>` can't order: they are grouped by case and placed after the other values (before them in descending
+  order).
 
 ### Finding things: `first`, `find` and `required`
 
diff --git a/src/Collections/Internal/containers.php b/src/Collections/Internal/containers.php
index bf1d746..fac6140 100644
--- a/src/Collections/Internal/containers.php
+++ b/src/Collections/Internal/containers.php
@@ -147,6 +147,28 @@ function entries(iterable $iterable): array
     return $entries;
 }
 
+/**
+ * Builds a `Ds\Map` from entries given by position, in the order of the keys of $order (positions).
+ *
+ * @internal
+ *
+ * @param list<mixed>       $keys
+ * @param array<int, mixed> $values
+ * @param array<int, mixed> $order
+ *
+ * @return \Ds\Map<mixed, mixed>
+ */
+function mapInOrder(array $keys, array $values, array $order): \Ds\Map
+{
+    $result = new \Ds\Map();
+    $result->allocate(count($order));
+    foreach ($order as $position => $_) {
+        $result->put($keys[$position], $values[$position]);
+    }
+
+    return $result;
+}
+
 /**
  * Yields [key, value] pairs back as key => value.
  *
diff --git a/src/Collections/transforms.php b/src/Collections/transforms.php
index d374036..d536e99 100644
--- a/src/Collections/transforms.php
+++ b/src/Collections/transforms.php
@@ -27,6 +27,7 @@ use function Kadet\Functional\Collections\Internal\iterated;
 use function Kadet\Functional\Collections\Internal\keyedLike;
 use function Kadet\Functional\Collections\Internal\seen;
 use function Kadet\Functional\Collections\Internal\listLike;
+use function Kadet\Functional\Collections\Internal\mapInOrder;
 use function Kadet\Functional\Collections\Internal\seqOf;
 use function Kadet\Functional\Collections\Internal\unpairs;
 use function Kadet\Functional\Collections\Internal\valuesOf;
@@ -314,14 +315,51 @@ function uniqueBy(callable $selector): \Closure
  */
 function sort(?callable $comparator = null): \Closure
 {
+    if ($comparator === null) {
+        // The native SORT_REGULAR sorts compare like `<=>` and are stable.
+        return static function (iterable $input): iterable {
+            if (is_array($input)) {
+                asort($input);
+
+                return $input;
+            }
+
+            if ($input instanceof \Ds\Map) {
+                $keys   = $input->keys()->toArray();
+                $values = $input->values()->toArray();
+                asort($values);
+
+                return mapInOrder($keys, $values, $values);
+            }
+
+            $values = valuesOf($input);
+            \sort($values);
+
+            return listLike($input, $values);
+        };
+    }
+
     // Comparators always take two values, so they are compiled without the ($value, $key) adaptation.
-    $comparator = $comparator === null ? static fn ($a, $b) => $a <=> $b : compile($comparator);
+    $comparator = compile($comparator);
 
     return static function (iterable $input) use ($comparator): iterable {
-        $entries = entries($input);
-        usort($entries, static fn ($a, $b) => $comparator($a[1], $b[1]));
+        if (is_array($input)) {
+            uasort($input, $comparator);
 
-        return keyedLike($input, unpairs($entries));
+            return $input;
+        }
+
+        if ($input instanceof \Ds\Map) {
+            $entries = entries($input);
+            usort($entries, static fn ($a, $b) => $comparator($a[1], $b[1]));
+
+            return keyedLike($input, unpairs($entries));
+        }
+
+        $values = valuesOf($input);
+        usort($values, $comparator);
+
+        return listLike($input, $values);
     };
 }
 
@@ -348,16 +386,47 @@ function sortBy(callable $selector, bool $descending = false): \Closure
 {
     $selector = callback($selector);
 
+    // The selected values are sorted natively: SORT_REGULAR compares like `<=>`, and PHP's sorts are stable, also
+    // arsort() for ties.
     return static function (iterable $input) use ($selector, $descending): iterable {
-        $entries = [];
-        foreach ($input as $key => $value) {
-            $entries[] = [$key, $value, $selector($value, $key)];
+        if (is_array($input)) {
+            $order = [];
+            foreach ($input as $key => $value) {
+                $order[$key] = $selector($value, $key);
+            }
+
+            $descending ? arsort($order) : asort($order);
+
+            $result = [];
+            foreach ($order as $key => $_) {
+                $result[$key] = $input[$key];
+            }
+
+            return $result;
         }
 
-        $direction = $descending ? -1 : 1;
-        usort($entries, static fn ($a, $b) => $direction * ($a[2] <=> $b[2]));
+        // Keys of `Ds\Map` can be objects, so the entries are sorted by position.
+        $keys   = [];
+        $values = [];
+        $order  = [];
+        foreach (iterated($input) as $key => $value) {
+            $keys[]   = $key;
+            $values[] = $value;
+            $order[]  = $selector($value, $key);
+        }
 
-        return keyedLike($input, unpairs($entries));
+        $descending ? arsort($order) : asort($order);
+
+        if ($input instanceof \Ds\Map) {
+            return mapInOrder($keys, $values, $order);
+        }
+
+        $result = [];
+        foreach ($order as $position => $_) {
+            $result[] = $values[$position];
+        }
+
+        return listLike($input, $result);
     };
 }
 
diff --git a/tests/Collections/TransformsTest.php b/tests/Collections/TransformsTest.php
index 2b77568..64e56c3 100644
--- a/tests/Collections/TransformsTest.php
+++ b/tests/Collections/TransformsTest.php
@@ -248,6 +248,81 @@ class TransformsTest extends \PHPUnit\Framework\TestCase
         $this->assertSame(['b' => 1, 'a' => 2], c\sortBy(fn ($v, $k) => $k, true)(['a' => 2, 'b' => 1]));
     }
 
+    public function testSortByIsStableForTies()
+    {
+        $items = [['k' => 1, 'n' => 'a'], ['k' => 0, 'n' => 'b'], ['k' => 1, 'n' => 'c'], ['k' => 0, 'n' => 'd'], ['k' => 1, 'n' => 'e']];
+
+        $this->assertSame(['b', 'd', 'a', 'c', 'e'], array_column(c\sortBy(fn ($o) => $o['k'])($items), 'n'));
+        $this->assertSame(['b', 'd', 'a', 'c', 'e'], array_column(c\sortBy(fn ($o) => $o['k'])(new Seq($items))->toArray(), 'n'));
+    }
+
+    public function testSortByDescendingIsStableForTies()
+    {
+        $items = [['k' => 0, 'n' => 'a'], ['k' => 1, 'n' => 'b'], ['k' => 0, 'n' => 'c'], ['k' => 1, 'n' => 'd'], ['k' => 0, 'n' => 'e']];
+
+        $this->assertSame(['b', 'd', 'a', 'c', 'e'], array_column(c\sortBy(fn ($o) => $o['k'], true)($items), 'n'));
+        $this->assertSame(['b', 'd', 'a', 'c', 'e'], array_column(c\sortBy(fn ($o) => $o['k'], true)(new Seq($items))->toArray(), 'n'));
+    }
+
+    public function testSortByWithDateTimeKeys()
+    {
+        $at    = fn (string $time) => new \DateTimeImmutable("2026-01-01 $time");
+        $items = ['c' => $at('10:00'), 'a' => $at('08:00'), 'd' => $at('10:00:01'), 'b' => $at('09:30')];
+
+        $this->assertSame(['a', 'b', 'c', 'd'], array_keys(c\sortBy(fn ($v) => $v)($items)));
+        $this->assertSame(['d', 'c', 'b', 'a'], array_keys(c\sortBy(fn ($v) => $v, true)($items)));
+    }
+
+    public function testSortByMixedNumericKeys()
+    {
+        $values = [3, 1.5, -2, 2.0, 0, 1, -0.5];
+
+        $this->assertSame([-2, -0.5, 0, 1, 1.5, 2.0, 3], c\sortBy(fn ($v) => $v)(new Seq($values))->toArray());
+        $this->assertSame([3, 2.0, 1.5, 1, 0, -0.5, -2], array_values(c\sortBy(fn ($v) => $v, true)($values)));
+    }
+
+    public function testSortAndSortByCompareLikeSpaceship()
+    {
+        $keys = [10, '9', 'abc', null, 2.5, '10', true, 'b', '', 0, [1, 2], [1], '1e1', ' 9', false];
+
+        $ascending = $keys;
+        usort($ascending, fn ($a, $b) => $a <=> $b);
+        $descending = $keys;
+        usort($descending, fn ($a, $b) => $b <=> $a);
+
+        $this->assertSame($ascending, array_values(c\sortBy(fn ($v) => $v)($keys)));
+        $this->assertSame($descending, array_values(c\sortBy(fn ($v) => $v, true)($keys)));
+        $this->assertSame($ascending, array_values(c\sort()($keys)));
+    }
+
+    public function testSortByKeepsObjectKeysOfMap()
+    {
+        $a   = new \stdClass();
+        $b   = new \stdClass();
+        $map = new Map();
+        $map->put($a, 2);
+        $map->put($b, 1);
+
+        $sorted = c\sortBy(fn ($v) => $v)($map);
+
+        $this->assertInstanceOf(Map::class, $sorted);
+        $this->assertSame([$b, $a], $sorted->keys()->toArray());
+        $this->assertSame([1, 2], $sorted->values()->toArray());
+    }
+
+    public function testSortByDoesNotMutateInput()
+    {
+        $array = ['x' => 3, 'y' => 1, 'z' => 2];
+        $seq   = new Seq([3, 1, 2]);
+
+        c\sortBy(fn ($v) => $v)($array);
+        c\sortBy(fn ($v) => $v, true)($seq);
+        c\sort()($array);
+
+        $this->assertSame(['x' => 3, 'y' => 1, 'z' => 2], $array);
+        $this->assertSame([3, 1, 2], $seq->toArray());
+    }
+
     public function testSortDoesNotMutateInput()
     {
         $seq = new Seq([3, 1, 2]);