diff --git a/kotlin/src/main/kotlin/net/jqwik/kotlin/api/BuildersExtensions.kt b/kotlin/src/main/kotlin/net/jqwik/kotlin/api/BuildersExtensions.kt
index a06674d57..b8c985650 100644
--- a/kotlin/src/main/kotlin/net/jqwik/kotlin/api/BuildersExtensions.kt
+++ b/kotlin/src/main/kotlin/net/jqwik/kotlin/api/BuildersExtensions.kt
@@ -9,7 +9,7 @@ import java.util.function.BiFunction
  * Convenience function for Kotlin to not use backticked `in` function.
  */
 @API(status = API.Status.EXPERIMENTAL, since = "1.6.0")
-fun <B, T> BuilderCombinator<B>.use(arbitrary: Arbitrary<T>, combinator: (B, T) -> B): BuilderCombinator<B>
+fun <B, T> BuilderCombinator<B>.use(arbitrary: Arbitrary<T & Any>, combinator: (B, T) -> B): BuilderCombinator<B>
     where B : Any {
     return this.use(arbitrary).`in`(combinator)
 }
diff --git a/kotlin/src/main/kotlin/net/jqwik/kotlin/api/CollectionExtensions.kt b/kotlin/src/main/kotlin/net/jqwik/kotlin/api/CollectionExtensions.kt
index 6e15b8d50..d084ee18a 100644
--- a/kotlin/src/main/kotlin/net/jqwik/kotlin/api/CollectionExtensions.kt
+++ b/kotlin/src/main/kotlin/net/jqwik/kotlin/api/CollectionExtensions.kt
@@ -9,10 +9,10 @@ import org.apiguardian.api.API
  * Convenience function to replace Arbitraries.subsetOf(..)
  */
 @API(status = API.Status.EXPERIMENTAL, since = "1.6.5")
-fun <T> Collection<T>.anySubset(): SetArbitrary<T> = Arbitraries.subsetOf(this)
+fun <T: Any> Collection<T>.anySubset(): SetArbitrary<T> = Arbitraries.subsetOf(this)
 
 /**
  * Convenience function to replace Arbitraries.of(..)
  */
 @API(status = API.Status.EXPERIMENTAL, since = "1.7.1")
-fun <T> Collection<T>.anyValue(): Arbitrary<T> = Arbitraries.of(this)
+fun <T: Any> Collection<T>.anyValue(): Arbitrary<T> = Arbitraries.of(this)
diff --git a/kotlin/src/main/kotlin/net/jqwik/kotlin/api/CombinatorDsl.kt b/kotlin/src/main/kotlin/net/jqwik/kotlin/api/CombinatorDsl.kt
index 8636b04ff..16fd0f0a8 100644
--- a/kotlin/src/main/kotlin/net/jqwik/kotlin/api/CombinatorDsl.kt
+++ b/kotlin/src/main/kotlin/net/jqwik/kotlin/api/CombinatorDsl.kt
@@ -63,13 +63,13 @@ class CombinatorScope internal constructor(private val bindings: ValueBindings)
         filters += filter
     }
 
-    fun <R> combineAs(creator: () -> R): Combined<R> {
+    fun <R> combineAs(creator: () -> R): Combined<R> where R : Any {
         check(!created.getAndSet(true)) { "'combineAs' must only be called once" }
 
         return Combined.Regular(arbitraries.toList(), filters.toList(), creator)
     }
 
-    fun <R> flatCombineAs(creator: () -> Arbitrary<R>): Combined<R> {
+    fun <R> flatCombineAs(creator: () -> Arbitrary<R>): Combined<R> where R : Any {
         check(!created.getAndSet(true)) { "'flatCombineAs' must only be called once" }
 
         return Combined.Flat(arbitraries.toList(), filters.toList(), creator)
@@ -102,7 +102,7 @@ sealed class Combined<R>(
         arbitraries: List<Arbitrary<*>>,
         filters: List<() -> Boolean>,
         val creator: () -> R
-    ) : Combined<R>(arbitraries, filters) {
+    ) : Combined<R>(arbitraries, filters) where R : Any {
         override fun ListCombinator<*>.asArbitrary(bindings: ValueBindings): Arbitrary<R> {
             return `as` { values ->
                 bindings.withValues(values) {
@@ -116,7 +116,7 @@ sealed class Combined<R>(
         arbitraries: List<Arbitrary<*>>,
         filters: List<() -> Boolean>,
         val creator: () -> Arbitrary<R>
-    ) : Combined<R>(arbitraries, filters) {
+    ) : Combined<R>(arbitraries, filters) where R: Any {
         override fun ListCombinator<*>.asArbitrary(bindings: ValueBindings): Arbitrary<R> {
             return flatAs { values ->
                 bindings.withValues(values) {
diff --git a/kotlin/src/main/kotlin/net/jqwik/kotlin/api/JqwikGlobals.kt b/kotlin/src/main/kotlin/net/jqwik/kotlin/api/JqwikGlobals.kt
index d0b88ae99..ce05e3791 100644
--- a/kotlin/src/main/kotlin/net/jqwik/kotlin/api/JqwikGlobals.kt
+++ b/kotlin/src/main/kotlin/net/jqwik/kotlin/api/JqwikGlobals.kt
@@ -28,7 +28,7 @@ fun <A, B, C> anyTriple(firstArbitrary: Arbitrary<A>, secondArbitrary: Arbitrary
 
 
 /**
- * Function to create a [FunctionWrapper].
+ * Function to create a [Functions.FunctionWrapper].
  *
  * This is a Kotlin convenience for [Functions.function] which requires a Java class instead.
  */
@@ -41,7 +41,7 @@ fun anyFunction(kClass: KClass<*>): Functions.FunctionWrapper {
  * Create a [FunctionArbitrary] for Kotlin function without parameters.
  */
 @API(status = API.Status.EXPERIMENTAL, since = "1.6.0")
-fun <R> anyFunction0(returning: Arbitrary<R>): FunctionArbitrary<Function0<R>, R> {
+fun <R> anyFunction0(returning: Arbitrary<out R>): FunctionArbitrary<Function0<R>, out R> {
     return anyFunction(Function0::class).returning(returning)
 }
 
@@ -49,7 +49,7 @@ fun <R> anyFunction0(returning: Arbitrary<R>): FunctionArbitrary<Function0<R>, R
  * Create a [FunctionArbitrary] for Kotlin function with 1 parameter.
  */
 @API(status = API.Status.EXPERIMENTAL, since = "1.6.0")
-fun <A, R> anyFunction1(returning: Arbitrary<R>): FunctionArbitrary<Function1<A, R>, R> {
+fun <A, R> anyFunction1(returning: Arbitrary<out R>): FunctionArbitrary<Function1<A, R>, out R> {
     return anyFunction(Function1::class).returning(returning)
 }
 
@@ -57,7 +57,7 @@ fun <A, R> anyFunction1(returning: Arbitrary<R>): FunctionArbitrary<Function1<A,
  * Create a [FunctionArbitrary] for Kotlin function with 2 parameters.
  */
 @API(status = API.Status.EXPERIMENTAL, since = "1.6.0")
-fun <A, B, R> anyFunction2(returning: Arbitrary<R>): FunctionArbitrary<Function2<A, B, R>, R> {
+fun <A, B, R> anyFunction2(returning: Arbitrary<out R>): FunctionArbitrary<Function2<A, B, R>, out R> {
     return anyFunction(Function2::class).returning(returning)
 }
 
@@ -65,7 +65,7 @@ fun <A, B, R> anyFunction2(returning: Arbitrary<R>): FunctionArbitrary<Function2
  * Create a [FunctionArbitrary] for Kotlin function with 3 parameters.
  */
 @API(status = API.Status.EXPERIMENTAL, since = "1.6.0")
-fun <A, B, C, R> anyFunction3(returning: Arbitrary<R>): FunctionArbitrary<Function3<A, B, C, R>, R> {
+fun <A, B, C, R> anyFunction3(returning: Arbitrary<out R>): FunctionArbitrary<Function3<A, B, C, R>, out R> {
     return anyFunction(Function3::class).returning(returning)
 }
 
@@ -73,7 +73,7 @@ fun <A, B, C, R> anyFunction3(returning: Arbitrary<R>): FunctionArbitrary<Functi
  * Create a [FunctionArbitrary] for Kotlin function with 4 parameters.
  */
 @API(status = API.Status.EXPERIMENTAL, since = "1.6.0")
-fun <A, B, C, D, R> anyFunction4(returning: Arbitrary<R>): FunctionArbitrary<Function4<A, B, C, D, R>, R> {
+fun <A, B, C, D, R> anyFunction4(returning: Arbitrary<out R>): FunctionArbitrary<Function4<A, B, C, D, R>, out R> {
     return anyFunction(Function4::class).returning(returning)
 }