diff --git a/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/Iterable.kt b/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/Iterable.kt
index 3804f9ee1df..8da56d0f1a1 100644
--- a/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/Iterable.kt
+++ b/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/Iterable.kt
@@ -287,13 +287,16 @@ inline fun <A, B> Iterable<A>.foldRight(initial: B, operation: (A, acc: B) -> B)
     else -> reversed().fold(initial) { acc, a -> operation(a, acc) }
   }
 
-inline fun <E, A, B> Iterable<A>.traverseEither(f: (A) -> Either<E, B>): Either<E, List<B>> =
-  foldRight<A, Either<E, List<B>>>(emptyList<B>().right()) { a, acc ->
+inline fun <E, A, B> Iterable<A>.traverseEither(f: (A) -> Either<E, B>): Either<E, List<B>> {
+  val acc = mutableListOf<B>()
+  forEach { a ->
     when (val res = f(a)) {
-      is Right -> acc.map { bs -> listOf(res.value) + bs }
-      is Left -> res
+      is Right -> acc.add(res.value)
+      is Left -> return@traverseEither res
     }
   }
+  return acc.right()
+}
 
 fun <E, A> Iterable<Either<E, A>>.sequenceEither(): Either<E, List<A>> =
   traverseEither(::identity)
@@ -302,15 +305,15 @@ inline fun <E, A, B> Iterable<A>.traverseValidated(
   semigroup: Semigroup<E>,
   f: (A) -> Validated<E, B>
 ): Validated<E, List<B>> = semigroup.run {
-  foldRight<A, Validated<E, List<B>>>(emptyList<B>().valid()) { a, acc ->
+  fold(Valid(mutableListOf<B>()) as Validated<E, MutableList<B>>) { acc, a ->
     when (val res = f(a)) {
       is Validated.Valid -> when (acc) {
-        is Validated.Valid -> acc.map { bs -> listOf(res.value) + bs }
-        is Validated.Invalid -> acc
+        is Valid -> acc.also { it.value.add(res.value) }
+        is Invalid -> acc
       }
       is Validated.Invalid -> when (acc) {
-        is Validated.Valid -> res
-        is Validated.Invalid -> Invalid(res.value.combine(acc.value))
+        is Valid -> res
+        is Invalid -> acc.value.combine(res.value).invalid()
       }
     }
   }
diff --git a/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/NonEmptyList.kt b/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/NonEmptyList.kt
index 2a039a3502b..e54e14853e8 100644
--- a/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/NonEmptyList.kt
+++ b/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/NonEmptyList.kt
@@ -412,13 +412,17 @@ fun <A, B, C> NonEmptyList<C>.unzip(f: (C) -> Pair<A, B>): Pair<NonEmptyList<A>,
     }
   }
 
-inline fun <E, A, B> NonEmptyList<A>.traverseEither(f: (A) -> Either<E, B>): Either<E, NonEmptyList<B>> =
-  foldRight(f(head).map(::nonEmptyListOf)) { a, acc ->
+inline fun <E, A, B> NonEmptyList<A>.traverseEither(f: (A) -> Either<E, B>): Either<E, NonEmptyList<B>> {
+  val acc = mutableListOf<B>()
+  forEach { a ->
     when (val res = f(a)) {
-      is Right -> acc.map { bs -> nonEmptyListOf(res.value) + bs }
-      is Left -> res
+      is Right -> acc.add(res.value)
+      is Left -> return@traverseEither res
     }
   }
+  // Safe due to traverse laws
+  return NonEmptyList.fromListUnsafe(acc).right()
+}
 
 fun <E, A> NonEmptyList<Either<E, A>>.sequenceEither(): Either<E, NonEmptyList<A>> =
   traverseEither(::identity)
@@ -427,18 +431,18 @@ inline fun <E, A, B> NonEmptyList<A>.traverseValidated(
   semigroup: Semigroup<E>,
   f: (A) -> Validated<E, B>
 ): Validated<E, NonEmptyList<B>> =
-  foldRight(f(head).map(::nonEmptyListOf)) { a, acc ->
+  fold(mutableListOf<B>().valid() as Validated<E, MutableList<B>>) { acc, a ->
     when (val res = f(a)) {
-      is Validated.Valid -> when (acc) {
-        is Validated.Valid -> acc.map { bs -> nonEmptyListOf(res.value) + bs }
-        is Validated.Invalid -> acc
+      is Valid -> when (acc) {
+        is Valid -> acc.also { it.value.add(res.value) }
+        is Invalid -> acc
       }
-      is Validated.Invalid -> when (acc) {
-        is Validated.Valid -> res
-        is Validated.Invalid -> Invalid(semigroup.run { res.value.combine(acc.value) })
+      is Invalid -> when (acc) {
+        is Valid -> res
+        is Invalid -> semigroup.run { acc.value.combine(res.value).invalid() }
       }
     }
-  }
+  }.map { NonEmptyList.fromListUnsafe(it) }
 
 fun <E, A> NonEmptyList<Validated<E, A>>.sequenceValidated(semigroup: Semigroup<E>): Validated<E, NonEmptyList<A>> =
   traverseValidated(semigroup, ::identity)
diff --git a/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/Sequence.kt b/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/Sequence.kt
index 8d4e6ee8468..4a8eae12f60 100644
--- a/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/Sequence.kt
+++ b/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/Sequence.kt
@@ -643,23 +643,35 @@ fun <A> Sequence<A>.split(): Pair<Sequence<A>, A>? =
 fun <A> Sequence<A>.tail(): Sequence<A> =
   drop(1)
 
-fun <E, A, B> Sequence<A>.traverseEither(f: (A) -> Either<E, B>): Either<E, Sequence<B>> =
-  foldRight<A, Either<E, Sequence<B>>>(Eval.now(sequenceOf<B>().right())) { a, eval ->
+fun <E, A, B> Sequence<A>.traverseEither(f: (A) -> Either<E, B>): Either<E, Sequence<B>> {
+  // Note: Using a mutable list here avoids the stackoverflows one can accidentally create when using
+  //  Sequence.plus instead. But we don't convert the sequence to a list beforehand to avoid
+  //  forcing too much of the sequence to be evaluated.
+  val acc = mutableListOf<B>()
+  forEach { a ->
     when (val res = f(a)) {
-      is Right -> eval.map { either ->
-        either.map { bs -> sequenceOf(res.value) + bs }
-      }
-      is Left -> Eval.now(res.value.left())
+      is Right -> acc.add(res.value)
+      is Left -> return@traverseEither res
     }
-  }.value()
+  }
+  return acc.asSequence().right()
+}
 
 fun <E, A, B> Sequence<A>.traverseValidated(
   semigroup: Semigroup<E>,
   f: (A) -> Validated<E, B>
-): Validated<E, Sequence<B>> =
-  foldRight<A, Validated<E, Sequence<B>>>(Eval.now(emptySequence<B>().valid())) { a, acc ->
-    acc.map { f(a).zip(semigroup, it) { b, bs -> sequenceOf(b) + bs } }
-  }.value()
+): Validated<E, Sequence<B>> = fold(mutableListOf<B>().valid() as Validated<E, MutableList<B>>) { acc, a ->
+  when (val res = f(a)) {
+    is Valid -> when (acc) {
+      is Valid -> acc.also { it.value.add(res.value) }
+      is Invalid -> acc
+    }
+    is Invalid -> when (acc) {
+      is Valid -> res
+      is Invalid -> semigroup.run { acc.value.combine(res.value).invalid() }
+    }
+  }
+}.map { it.asSequence() }
 
 /**
  * splits an union into its component parts.
diff --git a/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/map.kt b/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/map.kt
index aaed4901c3a..20f767571dc 100644
--- a/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/map.kt
+++ b/arrow-libs/core/arrow-core/src/main/kotlin/arrow/core/map.kt
@@ -189,13 +189,16 @@ fun <K, A, B> Map<K, A>.flatMap(f: (Map.Entry<K, A>) -> Map<K, B>): Map<K, B> =
     f(entry)[entry.key]?.let { Pair(entry.key, it) }.asIterable()
   }.toMap()
 
-inline fun <K, E, A, B> Map<K, A>.traverseEither(f: (A) -> Either<E, B>): Either<E, Map<K, B>> =
-  foldRight(emptyMap<K, B>().right()) { (k, a), acc: Either<E, Map<K, B>> ->
-    when (val res = f(a)) {
-      is Right -> acc.map { bs: Map<K, B> -> mapOf(k to res.value) + bs }
-      is Left -> res
+inline fun <K, E, A, B> Map<K, A>.traverseEither(f: (A) -> Either<E, B>): Either<E, Map<K, B>> {
+  val acc = mutableMapOf<K, B>()
+  forEach { (k, v) ->
+    when (val res = f(v)) {
+      is Right -> acc[k] = res.value
+      is Left -> return@traverseEither res
     }
   }
+  return acc.right()
+}
 
 fun <K, E, A> Map<K, Either<E, A>>.sequenceEither(): Either<E, Map<K, A>> =
   traverseEither(::identity)
@@ -203,19 +206,20 @@ fun <K, E, A> Map<K, Either<E, A>>.sequenceEither(): Either<E, Map<K, A>> =
 inline fun <K, E, A, B> Map<K, A>.traverseValidated(
   semigroup: Semigroup<E>,
   f: (A) -> Validated<E, B>
-): Validated<E, Map<K, B>> =
-  foldRight<K, A, Validated<E, Map<K, B>>>(emptyMap<K, B>().valid()) { (k, a), acc ->
-    when (val res = f(a)) {
-      is Validated.Valid -> when (acc) {
-        is Validated.Valid -> acc.map { bs -> mapOf(k to res.value) + bs }
-        is Validated.Invalid -> acc
+): Validated<E, Map<K, B>> {
+  return foldLeft(mutableMapOf<K, B>().valid() as Validated<E, MutableMap<K, B>>) { acc, (k, v) ->
+    when (val res = f(v)) {
+      is Valid -> when (acc) {
+        is Valid -> acc.also { it.value[k] = res.value }
+        is Invalid -> acc
       }
-      is Validated.Invalid -> when (acc) {
-        is Validated.Valid -> res
-        is Validated.Invalid -> Invalid(semigroup.run { res.value.combine(acc.value) })
+      is Invalid -> when (acc) {
+        is Valid -> res
+        is Invalid -> semigroup.run { acc.value.combine(res.value).invalid() }
       }
     }
   }
+}
 
 fun <K, E, A> Map<K, Validated<E, A>>.sequenceValidated(semigroup: Semigroup<E>): Validated<E, Map<K, A>> =
   traverseValidated(semigroup, ::identity)
diff --git a/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/IterableTest.kt b/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/IterableTest.kt
index 5ea5204c00f..5b437b1f96c 100644
--- a/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/IterableTest.kt
+++ b/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/IterableTest.kt
@@ -12,20 +12,42 @@ import kotlin.math.min
 class IterableTest : UnitSpec() {
   init {
     "traverseEither stack-safe" {
-      (0..20_000).map { Either.Right(it) }
-        .sequenceEither() shouldBe Either.Right((0..20_000).toList())
+      // also verifies result order and execution order (l to r)
+      val acc = mutableListOf<Int>()
+      val res = (0..20_000).traverseEither { a ->
+        acc.add(a)
+        Either.Right(a)
+      }
+      res shouldBe Either.Right(acc)
+      res shouldBe Either.Right((0..20_000).toList())
     }
 
     "traverseEither short-circuit" {
       forAll(Gen.list(Gen.int())) { ints ->
-        (ints.map { Either.Right(it) } + Either.Left(Unit))
-          .sequenceEither() == Either.Left(Unit)
+        val acc = mutableListOf<Int>()
+        val evens = ints.traverseEither {
+          if (it % 2 == 0) {
+            acc.add(it)
+            Either.Right(it)
+          } else Either.Left(it)
+        }
+        acc == ints.takeWhile { it % 2 == 0 } &&
+          when (evens) {
+            is Either.Right -> evens.value == ints
+            is Either.Left -> evens.value == ints.first { it % 2 != 0 }
+          }
       }
     }
 
     "traverseValidated stack-safe" {
-      (0..20_000).map { Validated.Valid(it) }
-        .sequenceValidated(Semigroup.string()) shouldBe Validated.Valid((0..20_000).toList())
+      // also verifies result order and execution order (l to r)
+      val acc = mutableListOf<Int>()
+      val res = (0..20_000).traverseValidated(Semigroup.string()) {
+        acc.add(it)
+        Validated.Valid(it)
+      }
+      res shouldBe Validated.Valid(acc)
+      res shouldBe Validated.Valid((0..20_000).toList())
     }
 
     "traverseValidated acummulates" {
diff --git a/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/MapKTest.kt b/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/MapKTest.kt
index b4e9fc92015..12d19dd9a1a 100644
--- a/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/MapKTest.kt
+++ b/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/MapKTest.kt
@@ -8,12 +8,63 @@ import arrow.typeclasses.Monoid
 import arrow.typeclasses.Semigroup
 import io.kotlintest.properties.Gen
 import io.kotlintest.properties.forAll
+import io.kotlintest.shouldBe
 
 class MapKTest : UnitSpec() {
 
   init {
     testLaws(MonoidLaws.laws(Monoid.map(Semigroup.int()), Gen.map(Gen.longSmall(), Gen.intSmall())))
 
+    "traverseEither is stacksafe" {
+      val acc = mutableListOf<Int>()
+      val res = (0..20_000).map { it to it }.toMap().traverseEither { v ->
+        acc.add(v)
+        Either.Right(v)
+      }
+      res shouldBe acc.map { it to it }.toMap().right()
+      res shouldBe (0..20_000).map { it to it }.toMap().right()
+    }
+
+    "traverseEither short-circuit" {
+      forAll(Gen.map(Gen.int(), Gen.int())) { ints ->
+        val acc = mutableListOf<Int>()
+        val evens = ints.traverseEither {
+          if (it % 2 == 0) {
+            acc.add(it)
+            Either.Right(it)
+          } else Either.Left(it)
+        }
+        acc == ints.values.takeWhile { it % 2 == 0 } &&
+          when (evens) {
+            is Either.Right -> evens.value == ints
+            is Either.Left -> evens.value == ints.values.first { it % 2 != 0 }
+          }
+      }
+    }
+
+    "traverseValidated is stacksafe" {
+      val acc = mutableListOf<Int>()
+      val res = (0..20_000).map { it to it }.toMap().traverseValidated(Semigroup.string()) { v ->
+        acc.add(v)
+        Validated.Valid(v)
+      }
+      res shouldBe acc.map { it to it }.toMap().valid()
+      res shouldBe (0..20_000).map { it to it }.toMap().valid()
+    }
+
+    "traverseValidated acummulates" {
+      forAll(Gen.map(Gen.int(), Gen.int())) { ints ->
+        val res: ValidatedNel<Int, Map<Int, Int>> =
+          ints.traverseValidated(Semigroup.nonEmptyList()) { i -> if (i % 2 == 0) i.validNel() else i.invalidNel() }
+
+        val expected: ValidatedNel<Int, Map<Int, Int>> =
+          NonEmptyList.fromList(ints.values.filterNot { it % 2 == 0 })
+            .fold({ ints.entries.filter { (_, v) -> v % 2 == 0 }.map { (k, v) -> k to v }.toMap().validNel() }, { it.invalid() })
+
+        res == expected
+      }
+    }
+
     "can align maps" {
       // aligned keySet is union of a's and b's keys
       forAll(Gen.map(Gen.long(), Gen.bool()), Gen.map(Gen.long(), Gen.bool())) { a, b ->
diff --git a/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/NonEmptyListTest.kt b/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/NonEmptyListTest.kt
index 94da056547d..9e78a8eec5e 100644
--- a/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/NonEmptyListTest.kt
+++ b/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/NonEmptyListTest.kt
@@ -6,6 +6,7 @@ import arrow.core.test.laws.SemigroupLaws
 import arrow.typeclasses.Semigroup
 import io.kotlintest.properties.Gen
 import io.kotlintest.properties.forAll
+import io.kotlintest.shouldBe
 import kotlin.math.max
 import kotlin.math.min
 
@@ -14,6 +15,57 @@ class NonEmptyListTest : UnitSpec() {
 
     testLaws(SemigroupLaws.laws(Semigroup.nonEmptyList(), Gen.nonEmptyList(Gen.int())))
 
+    "traverseEither stack-safe" {
+      // also verifies result order and execution order (l to r)
+      val acc = mutableListOf<Int>()
+      val res = NonEmptyList.fromListUnsafe((0..20_000).toList()).traverseEither { a ->
+        acc.add(a)
+        Either.Right(a)
+      }
+      res shouldBe Either.Right(NonEmptyList.fromListUnsafe(acc))
+      res shouldBe Either.Right(NonEmptyList.fromListUnsafe((0..20_000).toList()))
+    }
+
+    "traverseEither short-circuit" {
+      forAll(Gen.nonEmptyList(Gen.int())) { ints ->
+        val acc = mutableListOf<Int>()
+        val evens = ints.traverseEither {
+          if (it % 2 == 0) {
+            acc.add(it)
+            Either.Right(it)
+          } else Either.Left(it)
+        }
+        acc == ints.takeWhile { it % 2 == 0 } &&
+          when (evens) {
+            is Either.Right -> evens.value == ints
+            is Either.Left -> evens.value == ints.first { it % 2 != 0 }
+          }
+      }
+    }
+
+    "traverseValidated stack-safe" {
+      // also verifies result order and execution order (l to r)
+      val acc = mutableListOf<Int>()
+      val res = (0..20_000).traverseValidated(Semigroup.string()) {
+        acc.add(it)
+        Validated.Valid(it)
+      }
+      res shouldBe Validated.Valid(acc)
+      res shouldBe Validated.Valid((0..20_000).toList())
+    }
+
+    "traverseValidated acummulates" {
+      forAll(Gen.nonEmptyList(Gen.int())) { ints ->
+        val res: ValidatedNel<Int, NonEmptyList<Int>> =
+          ints.traverseValidated(Semigroup.nonEmptyList()) { i -> if (i % 2 == 0) i.validNel() else i.invalidNel() }
+
+        val expected: ValidatedNel<Int, NonEmptyList<Int>> = NonEmptyList.fromList(ints.filterNot { it % 2 == 0 })
+          .fold({ NonEmptyList.fromListUnsafe(ints.filter { it % 2 == 0 }).validNel() }, { it.invalid() })
+
+        res == expected
+      }
+    }
+
     "can align lists with different lengths" {
       forAll(Gen.nonEmptyList(Gen.bool()), Gen.nonEmptyList(Gen.bool())) { a, b ->
         a.align(b).size == max(a.size, b.size)
diff --git a/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/SequenceKTest.kt b/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/SequenceKTest.kt
index 04f33b86445..25045568c9a 100644
--- a/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/SequenceKTest.kt
+++ b/arrow-libs/core/arrow-core/src/test/kotlin/arrow/core/SequenceKTest.kt
@@ -4,6 +4,7 @@ import arrow.core.test.UnitSpec
 import arrow.core.test.generators.sequence
 import arrow.core.test.laws.MonoidLaws
 import arrow.typeclasses.Monoid
+import arrow.typeclasses.Semigroup
 import io.kotlintest.matchers.sequences.shouldBeEmpty
 import io.kotlintest.properties.Gen
 import io.kotlintest.properties.forAll
@@ -17,10 +18,43 @@ class SequenceKTest : UnitSpec() {
 
     testLaws(MonoidLaws.laws(Monoid.sequence(), Gen.sequence(Gen.int())) { s1, s2 -> s1.toList() == s2.toList() })
 
-    "traverseEither is stacksafe over very long collections and short circuits properly" {
-      // This has to traverse 30k elements till it reaches None and terminates
-      generateSequence(0) { it + 1 }.map { if (it < 20_000) Either.Right(it) else Either.Left(Unit) }
-        .sequenceEither() shouldBe Either.Left(Unit)
+    "traverseEither stack-safe" {
+      // also verifies result order and execution order (l to r)
+      val acc = mutableListOf<Int>()
+      val res = generateSequence(0) { it + 1 }.traverseEither { a ->
+        if (a > 20_000) {
+          Either.Left(Unit)
+        } else {
+          acc.add(a)
+          Either.Right(a)
+        }
+      }
+      acc shouldBe (0..20_000).toList()
+      res shouldBe Either.Left(Unit)
+    }
+
+    "traverseValidated stack-safe" {
+      // also verifies result order and execution order (l to r)
+      val acc = mutableListOf<Int>()
+      val res = (0..20_000).asSequence().traverseValidated(Semigroup.string()) {
+        acc.add(it)
+        Validated.Valid(it)
+      }.map { it.toList() }
+      res shouldBe Validated.Valid(acc)
+      res shouldBe Validated.Valid((0..20_000).toList())
+    }
+
+    "traverseValidated acummulates" {
+      forAll(Gen.list(Gen.int())) { ints ->
+        val ints = ints.asSequence()
+        val res: ValidatedNel<Int, Sequence<Int>> = ints.map { i -> if (i % 2 == 0) i.validNel() else i.invalidNel() }
+          .sequenceValidated(Semigroup.nonEmptyList())
+
+        val expected: ValidatedNel<Int, Sequence<Int>> = NonEmptyList.fromList(ints.filterNot { it % 2 == 0 }.toList())
+          .fold({ ints.filter { it % 2 == 0 }.validNel() }, { it.invalid() })
+
+        res.map { it.toList() } == expected.map { it.toList() }
+      }
     }
 
     "zip3" {