diff --git a/src/run_program.rs b/src/run_program.rs
index c9f51ddf..d8cfb7fe 100644
--- a/src/run_program.rs
+++ b/src/run_program.rs
@@ -1,5 +1,5 @@
-use super::traverse_path::traverse_path;
-use crate::allocator::{Allocator, Checkpoint, NodePtr, SExp};
+use super::traverse_path::{traverse_path, traverse_path_fast};
+use crate::allocator::{Allocator, Checkpoint, NodePtr, NodeVisitor, SExp};
 use crate::cost::Cost;
 use crate::dialect::{Dialect, OperatorSet};
 use crate::err_utils::err;
@@ -279,7 +279,15 @@ impl<'a, D: Dialect> RunProgramContext<'a, D> {
         // put a bunch of ops on op_stack
         let SExp::Pair(op_node, op_list) = self.allocator.sexp(program) else {
             // the program is just a bitfield path through the env tree
-            let r: Reduction = traverse_path(self.allocator, self.allocator.atom(program), env)?;
+            let r: Reduction = self.allocator.visit_node(program, |node| -> Response {
+                match node {
+                    NodeVisitor::Buffer(buf) => traverse_path(self.allocator, buf, env),
+                    NodeVisitor::U32(val) => traverse_path_fast(self.allocator, *val, env),
+                    NodeVisitor::Pair(_, _) => {
+                        panic!("expected atom, got pair");
+                    }
+                }
+            })?;
             self.push(r.1)?;
             return Ok(r.0);
         };
diff --git a/src/traverse_path.rs b/src/traverse_path.rs
index 27127397..fa47b0dc 100644
--- a/src/traverse_path.rs
+++ b/src/traverse_path.rs
@@ -72,6 +72,42 @@ pub fn traverse_path(allocator: &Allocator, node_index: &[u8], args: NodePtr) ->
     Ok(Reduction(cost, arg_list))
 }
 
+// The cost calculation for this version of traverse_path assumes the node_index has the canonical
+// integer representation (which is true for SmallAtom in the allocator). If there are any
+// redundant leading zeros, the slow path must be used
+pub fn traverse_path_fast(allocator: &Allocator, mut node_index: u32, args: NodePtr) -> Response {
+    if node_index == 0 {
+        return Ok(Reduction(
+            TRAVERSE_BASE_COST + TRAVERSE_COST_PER_BIT,
+            allocator.nil(),
+        ));
+    }
+
+    let mut arg_list: NodePtr = args;
+
+    let mut cost: Cost = TRAVERSE_BASE_COST + TRAVERSE_COST_PER_BIT;
+    let mut num_bits = 0;
+    while node_index != 1 {
+        let SExp::Pair(left, right) = allocator.sexp(arg_list) else {
+            return Err(EvalErr(arg_list, "path into atom".into()));
+        };
+
+        let is_bit_set: bool = (node_index & 0x01) != 0;
+        arg_list = if is_bit_set { right } else { left };
+        node_index >>= 1;
+        num_bits += 1
+    }
+
+    cost += num_bits * TRAVERSE_COST_PER_BIT;
+    // since positive numbers sometimes need a leading zero, e.g. 0x80, 0x8000 etc. We also
+    // need to add the cost of that leading zero byte
+    if num_bits == 7 || num_bits == 15 || num_bits == 23 || num_bits == 31 {
+        cost += TRAVERSE_COST_PER_ZERO_BYTE;
+    }
+
+    Ok(Reduction(cost, arg_list))
+}
+
 #[test]
 fn test_msb_mask() {
     assert_eq!(msb_mask(0x0), 0x0);
@@ -166,3 +202,61 @@ fn test_traverse_path() {
         EvalErr(n2, "path into atom".to_string())
     );
 }
+
+#[test]
+fn test_traverse_path_fast_fast() {
+    use crate::allocator::Allocator;
+
+    let mut a = Allocator::new();
+    let nul = a.nil();
+    let n1 = a.new_atom(&[0, 1, 2]).unwrap();
+    let n2 = a.new_atom(&[4, 5, 6]).unwrap();
+
+    assert_eq!(traverse_path_fast(&a, 0, n1).unwrap(), Reduction(44, nul));
+    assert_eq!(traverse_path_fast(&a, 0b1, n1).unwrap(), Reduction(44, n1));
+    assert_eq!(traverse_path_fast(&a, 0b1, n2).unwrap(), Reduction(44, n2));
+
+    let n3 = a.new_pair(n1, n2).unwrap();
+    assert_eq!(traverse_path_fast(&a, 0b1, n3).unwrap(), Reduction(44, n3));
+    assert_eq!(traverse_path_fast(&a, 0b10, n3).unwrap(), Reduction(48, n1));
+    assert_eq!(traverse_path_fast(&a, 0b11, n3).unwrap(), Reduction(48, n2));
+    assert_eq!(traverse_path_fast(&a, 0b11, n3).unwrap(), Reduction(48, n2));
+
+    let list = a.new_pair(n1, nul).unwrap();
+    let list = a.new_pair(n2, list).unwrap();
+
+    assert_eq!(
+        traverse_path_fast(&a, 0b10, list).unwrap(),
+        Reduction(48, n2)
+    );
+    assert_eq!(
+        traverse_path_fast(&a, 0b101, list).unwrap(),
+        Reduction(52, n1)
+    );
+    assert_eq!(
+        traverse_path_fast(&a, 0b111, list).unwrap(),
+        Reduction(52, nul)
+    );
+
+    // errors
+    assert_eq!(
+        traverse_path_fast(&a, 0b1011, list).unwrap_err(),
+        EvalErr(nul, "path into atom".to_string())
+    );
+    assert_eq!(
+        traverse_path_fast(&a, 0b1101, list).unwrap_err(),
+        EvalErr(n1, "path into atom".to_string())
+    );
+    assert_eq!(
+        traverse_path_fast(&a, 0b1001, list).unwrap_err(),
+        EvalErr(n1, "path into atom".to_string())
+    );
+    assert_eq!(
+        traverse_path_fast(&a, 0b1010, list).unwrap_err(),
+        EvalErr(n2, "path into atom".to_string())
+    );
+    assert_eq!(
+        traverse_path_fast(&a, 0b1110, list).unwrap_err(),
+        EvalErr(n2, "path into atom".to_string())
+    );
+}