diff --git a/catgrad-llm/src/utils/mod.rs b/catgrad-llm/src/utils/mod.rs
index 68dfe33b..6b3917a0 100644
--- a/catgrad-llm/src/utils/mod.rs
+++ b/catgrad-llm/src/utils/mod.rs
@@ -2,7 +2,7 @@ use catgrad::prelude::Dtype;
 use hf_hub::{Repo, RepoType, api::sync::ApiBuilder};
 use rayon::prelude::*;
 use serde::de::DeserializeOwned;
-use std::collections::{HashMap, HashSet};
+use std::collections::{BTreeMap, HashSet};
 use std::io::Read;
 use std::path::{Path, PathBuf};
 use tokenizers::tokenizer::Tokenizer;
@@ -535,8 +535,8 @@ pub fn load_model_weights<B: interpreter::Backend>(
     }
 
     // Read each tensor
-    let mut type_map = HashMap::new();
-    let mut data_map = HashMap::new();
+    let mut type_map = BTreeMap::new();
+    let mut data_map = BTreeMap::new();
     let mut total_params = 0;
 
     for file_path in model_paths {
diff --git a/catgrad/examples/hidden.rs b/catgrad/examples/hidden.rs
index f7ed3f11..80da9c1d 100644
--- a/catgrad/examples/hidden.rs
+++ b/catgrad/examples/hidden.rs
@@ -1,7 +1,7 @@
 use catgrad::prelude::ops::*;
 use catgrad::prelude::*;
 
-use std::collections::HashMap;
+use std::collections::BTreeMap;
 
 /// Construct, shapecheck, and interpret the `SimpleMNISTModel` using the ndarray backend.
 fn main() -> Result<(), Box<dyn std::error::Error>> {
@@ -167,7 +167,7 @@ fn load_param_types() -> typecheck::Parameters {
     use catgrad::category::core::Dtype;
     use catgrad::typecheck::value_types::{DtypeExpr, NatExpr, NdArrayType, ShapeExpr, TypeExpr};
 
-    let mut map = HashMap::new();
+    let mut map = BTreeMap::new();
 
     // Layer 1: (28*28) → 100
     let layer1_type = Type::Tensor(TypeExpr::NdArrayType(NdArrayType {
@@ -198,9 +198,9 @@ fn load_param_types() -> typecheck::Parameters {
 // NOTE: you would normally create this data by reading the safetensors file!
 fn load_param_data<B: interpreter::Backend>(backend: &B) -> interpreter::Parameters<B> {
     use catgrad::category::core::Shape;
-    use std::collections::HashMap;
+    use std::collections::BTreeMap;
 
-    let mut map = HashMap::new();
+    let mut map = BTreeMap::new();
 
     // Layer 1 weights: [784, 100] - initialize with small random-ish values
     let layer1_data: Vec<f32> = (0..784 * 100)
diff --git a/catgrad/src/abstract_interpreter/parameters.rs b/catgrad/src/abstract_interpreter/parameters.rs
index 8ad66633..85af0f0d 100644
--- a/catgrad/src/abstract_interpreter/parameters.rs
+++ b/catgrad/src/abstract_interpreter/parameters.rs
@@ -1,12 +1,9 @@
-//use super::backend::Backend;
-//use super::types::TaggedNdArray;
-
 use super::{Interpreter, Value};
 use crate::path::Path;
-use std::collections::HashMap;
+use std::collections::btree_map::{BTreeMap, Keys};
 
 #[derive(Clone, Debug)]
-pub struct Parameters<I: Interpreter>(pub HashMap<Path, Value<I>>);
+pub struct Parameters<I: Interpreter>(pub BTreeMap<Path, Value<I>>);
 
 // Needed so Backend doesn't have to implement Default
 impl<I: Interpreter> Default for Parameters<I> {
@@ -15,21 +12,21 @@ impl<I: Interpreter> Default for Parameters<I> {
     }
 }
 
-impl<I: Interpreter> From<HashMap<Path, Value<I>>> for Parameters<I> {
-    fn from(map: HashMap<Path, Value<I>>) -> Self {
+impl<I: Interpreter> From<BTreeMap<Path, Value<I>>> for Parameters<I> {
+    fn from(map: BTreeMap<Path, Value<I>>) -> Self {
         Parameters(map)
     }
 }
 
 impl<const N: usize, I: Interpreter> From<[(Path, Value<I>); N]> for Parameters<I> {
     fn from(arr: [(Path, Value<I>); N]) -> Self {
-        Parameters(HashMap::from(arr))
+        Parameters(BTreeMap::from(arr))
     }
 }
 
 impl<'a, I: Interpreter> IntoIterator for &'a Parameters<I> {
     type Item = &'a Path;
-    type IntoIter = std::collections::hash_map::Keys<'a, Path, Value<I>>;
+    type IntoIter = Keys<'a, Path, Value<I>>;
 
     fn into_iter(self) -> Self::IntoIter {
         self.0.keys()
@@ -37,7 +34,7 @@ impl<'a, I: Interpreter> IntoIterator for &'a Parameters<I> {
 }
 
 impl<I: Interpreter> Parameters<I> {
-    pub fn keys(&self) -> std::collections::hash_map::Keys<'_, Path, Value<I>> {
+    pub fn keys(&self) -> Keys<'_, Path, Value<I>> {
         self.0.keys()
     }
 }
diff --git a/catgrad/src/path.rs b/catgrad/src/path.rs
index 8beeaacf..9fdbd2ba 100644
--- a/catgrad/src/path.rs
+++ b/catgrad/src/path.rs
@@ -3,12 +3,12 @@ use std::fmt;
 use std::slice;
 
 #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
-#[derive(Debug, Clone, Hash, PartialEq, Eq)]
+#[derive(Debug, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
 pub struct Path(Vec<PathComponent>);
 
 // Names of definitions
 #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
-#[derive(Debug, Clone, Hash, PartialEq, Eq)]
+#[derive(Debug, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
 pub struct PathComponent(String); // only [a-zA-Z_]
 
 pub fn path(components: Vec<&str>) -> Result<Path, InvalidPathComponent> {