diff --git a/crates/trees/src/imt/mod.rs b/crates/trees/src/imt/mod.rs
index ea142fb..cf8a5bd 100644
--- a/crates/trees/src/imt/mod.rs
+++ b/crates/trees/src/imt/mod.rs
@@ -195,12 +195,13 @@ pub mod test {
     use keccak::keccak::Keccak256;
 
     #[test_case(0 => None)]
-    #[test_case(1 => Some(0))]
-    #[test_case(2 => Some(0))]
+    #[test_case(1 => None)]
+    #[test_case(2 => Some(1))]
     #[test_case(3 => Some(1))]
-    #[test_case(4 => Some(1))]
+    #[test_case(4 => Some(2))]
     #[test_case(5 => Some(2))]
-    #[test_case(6 => Some(2))]
+    #[test_case(6 => Some(3))]
+    #[test_case(27 => Some(13))]
     fn parent_of(index: usize) -> Option<usize> {
         parent(index)
     }
diff --git a/crates/trees/tests/equivalent.rs b/crates/trees/tests/equivalent.rs
new file mode 100644
index 0000000..49f6e44
--- /dev/null
+++ b/crates/trees/tests/equivalent.rs
@@ -0,0 +1,41 @@
+use keccak::keccak::Keccak256;
+use rand::{thread_rng, Rng};
+use trees::cascading::CascadingMerkleTree;
+use trees::imt::MerkleTree;
+use trees::lazy::{Canonical, LazyMerkleTree};
+
+const DEPTH: usize = 20;
+const DENSE_PREFIX: usize = 16;
+const EMPTY_VALUE: [u8; 32] = [0; 32];
+
+#[test]
+fn equivalent() {
+    let mut lazy: LazyMerkleTree<Keccak256, Canonical> =
+        LazyMerkleTree::<Keccak256, Canonical>::new_with_dense_prefix(
+            DEPTH,
+            DENSE_PREFIX,
+            &EMPTY_VALUE,
+        );
+    let mut lazy_derived = lazy.derived();
+    let mut imt: MerkleTree<Keccak256> = MerkleTree::new(DEPTH, EMPTY_VALUE);
+    let mut cascading: CascadingMerkleTree<Keccak256> =
+        CascadingMerkleTree::new(vec![], DEPTH, &EMPTY_VALUE);
+
+    assert_eq!(lazy.root(), imt.root());
+    assert_eq!(lazy.root(), cascading.root());
+
+    let mut rng = thread_rng();
+
+    let random_leaves = (0..1_000)
+        .map(|_| rng.gen::<[u8; 32]>())
+        .collect::<Vec<_>>();
+
+    for (i, leaf) in random_leaves.iter().enumerate() {
+        lazy_derived = lazy_derived.update(i, leaf);
+        imt.set(i, *leaf);
+        cascading.push(*leaf).unwrap();
+    }
+
+    assert_eq!(lazy_derived.root(), imt.root());
+    assert_eq!(lazy_derived.root(), cascading.root());
+}