diff --git a/src/Iterators/CachingIterator.php b/src/Iterators/CachingIterator.php
index 4c2830cb..30fc54fa 100644
--- a/src/Iterators/CachingIterator.php
+++ b/src/Iterators/CachingIterator.php
@@ -21,7 +21,7 @@
  * @property-read bool $empty
  * @property-read bool $odd
  * @property-read bool $even
- * @property-read int $counter
+ * @property-read int<0,max> $counter
  * @property-read TKey $nextKey
  * @property-read TValue $nextValue
  */
@@ -29,6 +29,7 @@ class CachingIterator extends \CachingIterator implements \Countable
 {
 	use Nette\SmartObject;
 
+	/** @var int<0, max> */
 	private int $counter = 0;
 
 
@@ -78,6 +79,7 @@ public function isEven(): bool
 	}
 
 
+	/** @return int<0, max> */
 	public function getCounter(): int
 	{
 		return $this->counter;
diff --git a/src/Utils/ArrayHash.php b/src/Utils/ArrayHash.php
index cb19b363..8b19a1c3 100644
--- a/src/Utils/ArrayHash.php
+++ b/src/Utils/ArrayHash.php
@@ -47,6 +47,7 @@ public function &getIterator(): \Iterator
 	}
 
 
+	/** @return int<0, max> */
 	public function count(): int
 	{
 		return count((array) $this);
diff --git a/src/Utils/ArrayList.php b/src/Utils/ArrayList.php
index 7852ce81..bbd4129e 100644
--- a/src/Utils/ArrayList.php
+++ b/src/Utils/ArrayList.php
@@ -50,6 +50,7 @@ public function &getIterator(): \Iterator
 	}
 
 
+	/** @return int<0, max> */
 	public function count(): int
 	{
 		return count($this->list);
diff --git a/src/Utils/Arrays.php b/src/Utils/Arrays.php
index 51916a60..7ebbf9e5 100644
--- a/src/Utils/Arrays.php
+++ b/src/Utils/Arrays.php
@@ -95,6 +95,7 @@ public static function mergeTree(array $array1, array $array2): array
 	/**
 	 * Returns zero-indexed position of given array key. Returns null if key is not found.
 	 * @param  array<mixed>  $array
+	 * @return ?int<0, max>
 	 */
 	public static function getKeyOffset(array $array, string|int $key): ?int
 	{
@@ -104,6 +105,7 @@ public static function getKeyOffset(array $array, string|int $key): ?int
 
 	/**
 	 * @param  array<mixed>  $array
+	 * @return ?int<0, max>
 	 * @deprecated  use  getKeyOffset()
 	 */
 	public static function searchKey(array $array, string|int $key): ?int
@@ -253,8 +255,9 @@ public static function renameKey(array &$array, string|int $oldKey, string|int $
 
 	/**
 	 * Returns only those array items, which matches a regular expression $pattern.
-	 * @param  string[]  $array
-	 * @return string[]
+	 * @template K of array-key
+	 * @param  array<K, string>  $array
+	 * @return array<K, string>
 	 */
 	public static function grep(
 		array $array,
@@ -271,7 +274,7 @@ public static function grep(
 	/**
 	 * Transforms multidimensional array to flat array.
 	 * @param  array<mixed>  $array
-	 * @return array<mixed>
+	 * @return ($preserveKeys is true ? array<mixed> : list<mixed>)
 	 */
 	public static function flatten(array $array, bool $preserveKeys = false): array
 	{
@@ -557,8 +560,9 @@ public static function toKey(mixed $value): int|string
 
 	/**
 	 * Returns a copy of $array where every item is cast to string and wrapped with $prefix and $suffix.
-	 * @param  string[]  $array
-	 * @return string[]
+	 * @template K of array-key
+	 * @param  array<K, string>  $array
+	 * @return array<K, string>
 	 */
 	public static function wrap(array $array, string $prefix = '', string $suffix = ''): array
 	{
diff --git a/src/Utils/Random.php b/src/Utils/Random.php
index f3ec874c..62f0c127 100644
--- a/src/Utils/Random.php
+++ b/src/Utils/Random.php
@@ -23,6 +23,7 @@ final class Random
 	/**
 	 * Generates a random string of given length from characters specified in second argument.
 	 * Supports intervals, such as `0-9` or `A-Z`.
+	 * @return non-empty-string
 	 */
 	public static function generate(int $length = 10, string $charlist = '0-9a-z'): string
 	{
diff --git a/src/Utils/Strings.php b/src/Utils/Strings.php
index d12d042e..b352f9a1 100644
--- a/src/Utils/Strings.php
+++ b/src/Utils/Strings.php
@@ -292,6 +292,7 @@ public static function indent(string $s, int $level = 1, string $chars = "\t"):
 
 	/**
 	 * Converts all characters of UTF-8 string to lower case.
+	 * @return ($s is non-empty-string ? non-empty-string : string)
 	 */
 	public static function lower(string $s): string
 	{
@@ -301,6 +302,7 @@ public static function lower(string $s): string
 
 	/**
 	 * Converts the first character of a UTF-8 string to lower case and leaves the other characters unchanged.
+	 * @return ($s is non-empty-string ? non-empty-string : string)
 	 */
 	public static function firstLower(string $s): string
 	{
@@ -310,6 +312,7 @@ public static function firstLower(string $s): string
 
 	/**
 	 * Converts all characters of a UTF-8 string to upper case.
+	 * @return ($s is non-empty-string ? non-empty-string : string)
 	 */
 	public static function upper(string $s): string
 	{
@@ -319,6 +322,7 @@ public static function upper(string $s): string
 
 	/**
 	 * Converts the first character of a UTF-8 string to upper case and leaves the other characters unchanged.
+	 * @return ($s is non-empty-string ? non-empty-string : string)
 	 */
 	public static function firstUpper(string $s): string
 	{
@@ -328,6 +332,7 @@ public static function firstUpper(string $s): string
 
 	/**
 	 * Converts the first character of every word of a UTF-8 string to upper case and the others to lower case.
+	 * @return ($s is non-empty-string ? non-empty-string : string)
 	 */
 	public static function capitalize(string $s): string
 	{
@@ -389,6 +394,7 @@ public static function findPrefix(array $strings): string
 	/**
 	 * Returns number of characters (not bytes) in UTF-8 string.
 	 * That is the number of Unicode code points which may differ from the number of graphemes.
+	 * @return ($s is non-empty-string ? int<1, max> : 0)
 	 */
 	public static function length(string $s): int
 	{
@@ -436,6 +442,7 @@ public static function padRight(string $s, int $length, string $pad = ' '): stri
 
 	/**
 	 * Reverses UTF-8 string.
+	 * @return ($s is non-empty-string ? non-empty-string : string)
 	 */
 	public static function reverse(string $s): string
 	{
@@ -479,6 +486,7 @@ public static function after(string $haystack, string $needle, int $nth = 1): ?s
 	/**
 	 * Returns position in characters of $nth occurence of $needle in $haystack or null if the $needle was not found.
 	 * Negative value of `$nth` means searching from the end.
+	 * @return ?int<0, max>
 	 */
 	public static function indexOf(string $haystack, string $needle, int $nth = 1): ?int
 	{
diff --git a/src/Utils/Validators.php b/src/Utils/Validators.php
index 2c583e75..18025f39 100644
--- a/src/Utils/Validators.php
+++ b/src/Utils/Validators.php
@@ -252,6 +252,7 @@ public static function isCallable(mixed $value): bool
 
 	/**
 	 * Checks if the value is a valid UTF-8 string.
+	 * @phpstan-assert-if-true string $value
 	 */
 	public static function isUnicode(mixed $value): bool
 	{
diff --git a/tests/Iterators/CachingIterator.basic.phpt b/tests/Iterators/CachingIterator.basic.phpt
index 9bdf0847..a50b3e66 100644
--- a/tests/Iterators/CachingIterator.basic.phpt
+++ b/tests/Iterators/CachingIterator.basic.phpt
@@ -69,3 +69,17 @@ test('', function () {
 	Assert::same(0, $iterator->getCounter());
 	Assert::true($iterator->isEmpty());
 });
+
+
+test('magic properties', function () {
+	$iterator = new Iterators\CachingIterator(['a' => 'Nette', 'b' => 'Framework']);
+	$iterator->rewind();
+	Assert::true($iterator->first);
+	Assert::false($iterator->last);
+	Assert::false($iterator->empty);
+	Assert::true($iterator->odd);
+	Assert::false($iterator->even);
+	Assert::same(1, $iterator->counter);
+	Assert::same('b', $iterator->nextKey);
+	Assert::same('Framework', $iterator->nextValue);
+});
diff --git a/tests/types/utils-types.php b/tests/types/utils-types.php
index 50a81ddf..ce6aecd5 100644
--- a/tests/types/utils-types.php
+++ b/tests/types/utils-types.php
@@ -6,7 +6,7 @@
  */
 
 use Nette\Iterators\CachingIterator;
-use Nette\Utils\{ArrayHash, Arrays, Helpers, Html, Iterables, Type, Validators};
+use Nette\Utils\{ArrayHash, ArrayList, Arrays, Helpers, Html, Iterables, Random, Strings, Type, Validators};
 use function PHPStan\Testing\assertType;
 
 
@@ -252,3 +252,87 @@ function testIterablesFirstKeyWithElse(iterable $iterable): void
 {
 	assertType('string', Iterables::firstKey($iterable, else: fn() => 'default'));
 }
+
+
+/** @param non-empty-string $nonEmpty */
+function testStringsLength(string $string, string $nonEmpty): void
+{
+	assertType('int<1, max>', Strings::length('abc'));
+	assertType('int<1, max>', Strings::length($nonEmpty));
+	assertType('0', Strings::length(''));
+	assertType('int<0, max>', Strings::length($string));
+}
+
+
+/** @param non-empty-string $nonEmpty */
+function testStringsCaseConversion(string $string, string $nonEmpty): void
+{
+	assertType('non-empty-string', Strings::lower($nonEmpty));
+	assertType('non-empty-string', Strings::firstLower($nonEmpty));
+	assertType('non-empty-string', Strings::upper('abc'));
+	assertType('non-empty-string', Strings::firstUpper($nonEmpty));
+	assertType('non-empty-string', Strings::capitalize($nonEmpty));
+	assertType('non-empty-string', Strings::reverse($nonEmpty));
+	assertType('string', Strings::lower($string));
+	assertType('string', Strings::reverse($string));
+}
+
+
+function testStringsIndexOf(string $string): void
+{
+	assertType('int<0, max>|null', Strings::indexOf($string, 'x'));
+}
+
+
+function testRandomGenerate(int $length): void
+{
+	assertType('non-empty-string', Random::generate());
+	assertType('non-empty-string', Random::generate($length, 'a-z'));
+}
+
+
+/** @param array<string, mixed> $array */
+function testArraysGetKeyOffset(array $array): void
+{
+	assertType('int<0, max>|null', Arrays::getKeyOffset($array, 'key'));
+}
+
+
+/** @param array<string, string> $array */
+function testArraysGrepAndWrap(array $array): void
+{
+	assertType('array<string, string>', Arrays::grep($array, '#x#'));
+	assertType('array<string, string>', Arrays::wrap($array, '<', '>'));
+	assertType('array<3|5, string>', Arrays::wrap([3 => 'a', 5 => 'b']));
+}
+
+
+/** @param array<string, mixed> $array */
+function testArraysFlatten(array $array, bool $preserveKeys): void
+{
+	assertType('list<mixed>', Arrays::flatten($array));
+	assertType('array<mixed>', Arrays::flatten($array, preserveKeys: true));
+	assertType('array<mixed>', Arrays::flatten($array, $preserveKeys));
+}
+
+
+/**
+ * @param ArrayHash<int> $hash
+ * @param ArrayList<int> $list
+ * @param CachingIterator<int, string> $iterator
+ */
+function testCounts(ArrayHash $hash, ArrayList $list, CachingIterator $iterator): void
+{
+	assertType('int<0, max>', $hash->count());
+	assertType('int<0, max>', $list->count());
+	assertType('int<0, max>', $iterator->getCounter());
+	assertType('int<0, max>', $iterator->counter);
+}
+
+
+function testValidatorsIsUnicode(mixed $value): void
+{
+	if (Validators::isUnicode($value)) {
+		assertType('string', $value);
+	}
+}