diff --git a/src/merkle/sparse_path.rs b/src/merkle/sparse_path.rs
index b641aa3..7022b40 100644
--- a/src/merkle/sparse_path.rs
+++ b/src/merkle/sparse_path.rs
@@ -75,6 +75,30 @@ impl SparseMerklePath {
     pub fn depth(&self) -> u8 {
         (self.nodes.len() + self.empty_nodes.count_ones() as usize) as u8
     }
+
+    /// Get a specific node in this path at a given depth.
+    pub fn get(&self, tree_depth: u8, node_depth: u8) -> RpoDigest {
+        let empty_bit = u64::checked_shl(1, node_depth.into()).unwrap();
+        let is_empty = (self.empty_nodes & empty_bit) != 0;
+
+        if is_empty {
+            return *EmptySubtreeRoots::entry(tree_depth, node_depth);
+        }
+
+        // Our index needs to account for all the empty nodes that aren't in `self.nodes`.
+        let nonempty_index: usize = {
+            // TODO: this could also be u64::unbounded_shl(1, node_depth + 1).wrapping_sub(1).
+            // We should check if that has any performance benefits over using 128-bit integers.
+            let mask: u64 = ((1u128 << (node_depth + 1)) - 1u128).try_into().unwrap();
+
+            let empty_before = u64::count_ones(self.empty_nodes & mask);
+            u64::checked_sub(node_depth as u64, empty_before as u64)
+                .unwrap()
+                .try_into()
+                .unwrap()
+        };
+        self.nodes[nonempty_index]
+    }
 }
 
 #[cfg(test)]
@@ -88,6 +112,19 @@ mod tests {
         Felt, Word, ONE,
     };
 
+    fn make_smt(pair_count: u64) -> Smt {
+        let entries: Vec<(RpoDigest, Word)> = (0..pair_count)
+            .map(|n| {
+                let leaf_index = ((n as f64 / pair_count as f64) * 255.0) as u64;
+                let key = RpoDigest::new([ONE, ONE, Felt::new(n), Felt::new(leaf_index)]);
+                let value = [ONE, ONE, ONE, ONE];
+                (key, value)
+            })
+            .collect();
+
+        Smt::with_entries(entries).unwrap()
+    }
+
     #[test]
     fn roundtrip() {
         let pair_count: u64 = 8192;
@@ -109,4 +146,20 @@ mod tests {
             assert_eq!(control_path, test_path);
         }
     }
+
+    #[test]
+    fn random_access() {
+        let tree = make_smt(8192);
+
+        for (i, (key, _value)) in tree.entries().enumerate() {
+            let control_path = tree.path(key);
+            let sparse_path = SparseMerklePath::from_path(SMT_DEPTH, control_path.clone());
+            assert_eq!(control_path.depth(), sparse_path.depth());
+
+            for (depth, control_node) in control_path.iter().enumerate() {
+                let test_node = sparse_path.get(SMT_DEPTH, depth as u8);
+                assert_eq!(*control_node, test_node, "at depth {depth} for entry {i}");
+            }
+        }
+    }
 }