diff --git a/zcash_primitives/src/merkle_tree.rs b/zcash_primitives/src/merkle_tree.rs
index e0b5861fa..0428248fc 100644
--- a/zcash_primitives/src/merkle_tree.rs
+++ b/zcash_primitives/src/merkle_tree.rs
@@ -194,10 +194,14 @@ impl<Node> CommitmentTree<Node> {
     }
 
     fn is_complete(&self, depth: usize) -> bool {
-        self.left.is_some()
-            && self.right.is_some()
-            && self.parents.len() == depth - 1
-            && self.parents.iter().all(|p| p.is_some())
+        if depth == 0 {
+            self.left.is_some() && self.right.is_none() && self.parents.is_empty()
+        } else {
+            self.left.is_some()
+                && self.right.is_some()
+                && self.parents.len() == depth - 1
+                && self.parents.iter().all(|p| p.is_some())
+        }
     }
 }
 
@@ -616,8 +620,8 @@ mod tests {
     use crate::sapling::{testing::arb_node, Node};
 
     use super::{
-        testing::arb_commitment_tree, CommitmentTree, Hashable, IncrementalWitness, MerklePath,
-        PathFiller,
+        testing::{arb_commitment_tree, TestNode},
+        CommitmentTree, Hashable, IncrementalWitness, MerklePath, PathFiller,
     };
 
     const HEX_EMPTY_ROOTS: [&str; 33] = [
@@ -1186,13 +1190,40 @@ mod tests {
             assert_eq!(frontier, frontier0);
         }
     }
+
+    #[test]
+    fn test_commitment_tree_complete() {
+        let mut t: CommitmentTree<TestNode> = CommitmentTree::empty();
+        for n in 1u64..=32 {
+            t.append(TestNode(n)).unwrap();
+            // every tree of a power-of-two height is complete
+            let is_complete = n.count_ones() == 1;
+            let level = 63 - n.leading_zeros(); //log2
+            assert_eq!(
+                is_complete,
+                t.is_complete(level.try_into().unwrap()),
+                "Tree {:?} {} complete at height {}",
+                t,
+                if is_complete {
+                    "should be"
+                } else {
+                    "should not be"
+                },
+                n
+            );
+        }
+    }
 }
 
 #[cfg(any(test, feature = "test-dependencies"))]
 pub mod testing {
+    use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
     use core::fmt::Debug;
     use proptest::collection::vec;
     use proptest::prelude::*;
+    use std::collections::hash_map::DefaultHasher;
+    use std::hash::Hasher;
+    use std::io::{self, Read, Write};
 
     use super::{CommitmentTree, Hashable};
 
@@ -1211,4 +1242,32 @@ pub mod testing {
             tree
         })
     }
+
+    #[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord)]
+    pub(crate) struct TestNode(pub(crate) u64);
+
+    impl Hashable for TestNode {
+        fn read<R: Read>(mut reader: R) -> io::Result<TestNode> {
+            reader.read_u64::<LittleEndian>().map(TestNode)
+        }
+
+        fn write<W: Write>(&self, mut writer: W) -> io::Result<()> {
+            writer.write_u64::<LittleEndian>(self.0)
+        }
+
+        fn combine(_: usize, a: &TestNode, b: &TestNode) -> TestNode {
+            let mut hasher = DefaultHasher::new();
+            hasher.write_u64(a.0);
+            hasher.write_u64(b.0);
+            TestNode(hasher.finish())
+        }
+
+        fn blank() -> TestNode {
+            TestNode(0)
+        }
+
+        fn empty_root(alt: usize) -> TestNode {
+            (0..alt).fold(Self::blank(), |v, lvl| Self::combine(lvl, &v, &v))
+        }
+    }
 }