diff --git a/stacks/arraystack/arraystack_test.go b/stacks/arraystack/arraystack_test.go
index 98af62c..fad4ac0 100644
--- a/stacks/arraystack/arraystack_test.go
+++ b/stacks/arraystack/arraystack_test.go
@@ -92,13 +92,20 @@ func TestStackPop(t *testing.T) {
 	}
 }
 
-func TestStackIterator(t *testing.T) {
+func TestStackIteratorOnEmpty(t *testing.T) {
+	stack := New()
+	it := stack.Iterator()
+	for it.Next() {
+		t.Errorf("Shouldn't iterate on empty stack")
+	}
+}
+
+func TestStackIteratorNext(t *testing.T) {
 	stack := New()
 	stack.Push("a")
 	stack.Push("b")
 	stack.Push("c")
 
-	// Iterator (next)
 	it := stack.Iterator()
 	count := 0
 	for it.Next() {
@@ -128,9 +135,18 @@ func TestStackIterator(t *testing.T) {
 	if actualValue, expectedValue := count, 3; actualValue != expectedValue {
 		t.Errorf("Got %v expected %v", actualValue, expectedValue)
 	}
+}
 
-	// Iterator (prev)
-	count = 0
+func TestStackIteratorPrev(t *testing.T) {
+	stack := New()
+	stack.Push("a")
+	stack.Push("b")
+	stack.Push("c")
+
+	it := stack.Iterator()
+	for it.Next() {
+	}
+	count := 0
 	for it.Prev() {
 		count++
 		index := it.Index()
@@ -158,12 +174,6 @@ func TestStackIterator(t *testing.T) {
 	if actualValue, expectedValue := count, 3; actualValue != expectedValue {
 		t.Errorf("Got %v expected %v", actualValue, expectedValue)
 	}
-
-	stack.Clear()
-	it = stack.Iterator()
-	for it.Next() {
-		t.Errorf("Shouldn't iterate on empty stack")
-	}
 }
 
 func BenchmarkStack(b *testing.B) {
diff --git a/stacks/linkedliststack/linkedliststack.go b/stacks/linkedliststack/linkedliststack.go
index 858033e..75f1948 100644
--- a/stacks/linkedliststack/linkedliststack.go
+++ b/stacks/linkedliststack/linkedliststack.go
@@ -108,7 +108,9 @@ func (stack *Stack) Iterator() Iterator {
 // If Next() returns true, then next element's index and value can be retrieved by Index() and Value().
 // Modifies the state of the iterator.
 func (iterator *Iterator) Next() bool {
-	iterator.index++
+	if iterator.index < iterator.stack.Size() {
+		iterator.index++
+	}
 	return iterator.stack.withinRange(iterator.index)
 }
 
diff --git a/trees/binaryheap/binaryheap.go b/trees/binaryheap/binaryheap.go
index 2bad245..0e5942f 100644
--- a/trees/binaryheap/binaryheap.go
+++ b/trees/binaryheap/binaryheap.go
@@ -44,7 +44,7 @@ import (
 
 func assertInterfaceImplementation() {
 	var _ trees.Tree = (*Heap)(nil)
-	var _ containers.IteratorWithIndex = (*Iterator)(nil)
+	var _ containers.ReverseIteratorWithIndex = (*Iterator)(nil)
 }
 
 // Heap holds elements in an array-list
@@ -129,7 +129,19 @@ func (heap *Heap) Iterator() Iterator {
 // If Next() returns true, then next element's index and value can be retrieved by Index() and Value().
 // Modifies the state of the iterator.
 func (iterator *Iterator) Next() bool {
-	iterator.index++
+	if iterator.index < iterator.heap.Size() {
+		iterator.index++
+	}
+	return iterator.heap.withinRange(iterator.index)
+}
+
+// Prev moves the iterator to the previous element and returns true if there was a previous element in the container.
+// If Prev() returns true, then previous element's index and value can be retrieved by Index() and Value().
+// Modifies the state of the iterator.
+func (iterator *Iterator) Prev() bool {
+	if iterator.index >= 0 {
+		iterator.index--
+	}
 	return iterator.heap.withinRange(iterator.index)
 }
 
diff --git a/trees/binaryheap/binaryheap_test.go b/trees/binaryheap/binaryheap_test.go
index 7699634..d72375a 100644
--- a/trees/binaryheap/binaryheap_test.go
+++ b/trees/binaryheap/binaryheap_test.go
@@ -107,19 +107,24 @@ func TestBinaryHeapRandom(t *testing.T) {
 	}
 }
 
-func TestBinaryHeapIterator(t *testing.T) {
+func TestBinaryHeapIteratorOnEmpty(t *testing.T) {
 	heap := NewWithIntComparator()
-
-	if actualValue := heap.Empty(); actualValue != true {
-		t.Errorf("Got %v expected %v", actualValue, true)
+	it := heap.Iterator()
+	for it.Next() {
+		t.Errorf("Shouldn't iterate on empty heap")
 	}
+}
 
+func TestBinaryHeapIteratorNext(t *testing.T) {
+	heap := NewWithIntComparator()
 	heap.Push(3) // [3]
 	heap.Push(2) // [2,3]
 	heap.Push(1) // [1,3,2](2 swapped with 1, hence last)
 
 	it := heap.Iterator()
+	count := 0
 	for it.Next() {
+		count++
 		index := it.Index()
 		value := it.Value()
 		switch index {
@@ -138,12 +143,51 @@ func TestBinaryHeapIterator(t *testing.T) {
 		default:
 			t.Errorf("Too many")
 		}
+		if actualValue, expectedValue := index, count-1; actualValue != expectedValue {
+			t.Errorf("Got %v expected %v", actualValue, expectedValue)
+		}
 	}
+	if actualValue, expectedValue := count, 3; actualValue != expectedValue {
+		t.Errorf("Got %v expected %v", actualValue, expectedValue)
+	}
+}
 
-	heap.Clear()
-	it = heap.Iterator()
+func TestBinaryHeapIteratorPrev(t *testing.T) {
+	heap := NewWithIntComparator()
+	heap.Push(3) // [3]
+	heap.Push(2) // [2,3]
+	heap.Push(1) // [1,3,2](2 swapped with 1, hence last)
+
+	it := heap.Iterator()
 	for it.Next() {
-		t.Errorf("Shouldn't iterate on empty stack")
+	}
+	count := 0
+	for it.Prev() {
+		count++
+		index := it.Index()
+		value := it.Value()
+		switch index {
+		case 0:
+			if actualValue, expectedValue := value, 1; actualValue != expectedValue {
+				t.Errorf("Got %v expected %v", actualValue, expectedValue)
+			}
+		case 1:
+			if actualValue, expectedValue := value, 3; actualValue != expectedValue {
+				t.Errorf("Got %v expected %v", actualValue, expectedValue)
+			}
+		case 2:
+			if actualValue, expectedValue := value, 2; actualValue != expectedValue {
+				t.Errorf("Got %v expected %v", actualValue, expectedValue)
+			}
+		default:
+			t.Errorf("Too many")
+		}
+		if actualValue, expectedValue := index, 3-count; actualValue != expectedValue {
+			t.Errorf("Got %v expected %v", actualValue, expectedValue)
+		}
+	}
+	if actualValue, expectedValue := count, 3; actualValue != expectedValue {
+		t.Errorf("Got %v expected %v", actualValue, expectedValue)
 	}
 }