diff --git a/.github/workflows/bench.yml b/.github/workflows/bench.yml
index d4d2c66c..e8e26384 100644
--- a/.github/workflows/bench.yml
+++ b/.github/workflows/bench.yml
@@ -16,7 +16,7 @@ jobs:
       - uses: actions/checkout@v2
       - uses: actions-rs/toolchain@v1
         with:
-          toolchain: 1.54.0
+          toolchain: 1.56.1
           override: true
       - name: Run benchmark
         run: cargo bench -- --output-format bencher | tee output.txt
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 7f0a5a8f..966cc8da 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -14,7 +14,7 @@ jobs:
       - uses: actions/checkout@v2
       - uses: actions-rs/toolchain@v1
         with:
-          toolchain: 1.54.0
+          toolchain: 1.56.1
           override: true
       - name: Run tests
         uses: actions-rs/cargo@v1
@@ -30,7 +30,7 @@ jobs:
       - uses: actions/checkout@v2
       - uses: actions-rs/toolchain@v1
         with:
-          toolchain: 1.54.0
+          toolchain: 1.56.1
           override: true
       # Build benchmarks to prevent bitrot
       - name: Build benchmarks
@@ -46,7 +46,7 @@ jobs:
       - uses: actions/checkout@v2
       - uses: actions-rs/toolchain@v1
         with:
-          toolchain: 1.54.0
+          toolchain: 1.56.1
           override: true
       - name: Setup mdBook
         uses: peaceiris/actions-mdbook@v1
@@ -89,7 +89,7 @@ jobs:
       - uses: actions/checkout@v2
       - uses: actions-rs/toolchain@v1
         with:
-          toolchain: 1.54.0
+          toolchain: 1.56.1
           override: true
       - name: cargo fetch
         uses: actions-rs/cargo@v1
@@ -112,7 +112,7 @@ jobs:
       - uses: actions/checkout@v2
       - uses: actions-rs/toolchain@v1
         with:
-          toolchain: 1.54.0
+          toolchain: 1.56.1
           override: true
       - run: rustup component add rustfmt
       - uses: actions-rs/cargo@v1
diff --git a/.github/workflows/lints-stable.yml b/.github/workflows/lints-stable.yml
index e91ea098..242041e8 100644
--- a/.github/workflows/lints-stable.yml
+++ b/.github/workflows/lints-stable.yml
@@ -5,19 +5,19 @@ on: pull_request
 
 jobs:
   clippy:
-    name: Clippy (1.54.0)
+    name: Clippy (1.56.1)
     timeout-minutes: 30
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v2
       - uses: actions-rs/toolchain@v1
         with:
-          toolchain: 1.54.0
+          toolchain: 1.56.1
           components: clippy
           override: true
       - name: Run Clippy
         uses: actions-rs/clippy-check@v1
         with:
-          name: Clippy (1.54.0)
+          name: Clippy (1.56.1)
           token: ${{ secrets.GITHUB_TOKEN }}
           args: --all-features --all-targets -- -D warnings
diff --git a/CHANGELOG.md b/CHANGELOG.md
index a8bfecfa..66f5d0e6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -40,3 +40,6 @@ and this project adheres to Rust's notion of
 
 ## [0.1.0-beta.1] - 2021-12-17
 Initial release!
+
+## [Removed]
+- The `std::hash::Hash` instance for `MerkleHashOrchard` has been removed.
diff --git a/Cargo.toml b/Cargo.toml
index fb72435f..5c88fe07 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -47,6 +47,9 @@ incrementalmerkletree = "0.2"
 # Developer tooling dependencies
 plotters = { version = "0.3.0", optional = true }
 
+[patch.crates-io]
+incrementalmerkletree = { git = "https://github.com/zcash/incrementalmerkletree.git", rev = "dd57b430dee7c0b163f4035fef2280cd1935036c" }
+
 [dev-dependencies]
 criterion = "0.3"
 halo2_gadgets = { version = "=0.1.0-beta.1", features = ["test-dependencies"] }
diff --git a/rust-toolchain b/rust-toolchain
index b7921ae8..43c989b5 100644
--- a/rust-toolchain
+++ b/rust-toolchain
@@ -1 +1 @@
-1.54.0
+1.56.1
diff --git a/src/builder.rs b/src/builder.rs
index 811d738e..4a207c2b 100644
--- a/src/builder.rs
+++ b/src/builder.rs
@@ -1,6 +1,7 @@
 //! Logic for building Orchard components of transactions.
 
 use std::convert::TryFrom;
+use std::fmt;
 use std::iter;
 
 use ff::Field;
@@ -363,9 +364,9 @@ impl Builder {
 }
 
 /// Marker trait representing bundle signatures in the process of being created.
-pub trait InProgressSignatures {
+pub trait InProgressSignatures: fmt::Debug {
     /// The authorization type of an Orchard action in the process of being authorized.
-    type SpendAuth;
+    type SpendAuth: fmt::Debug;
 }
 
 /// Marker for a bundle in the process of being built.
@@ -375,7 +376,7 @@ pub struct InProgress<P, S: InProgressSignatures> {
     sigs: S,
 }
 
-impl<P, S: InProgressSignatures> Authorization for InProgress<P, S> {
+impl<P: fmt::Debug, S: InProgressSignatures> Authorization for InProgress<P, S> {
     type SpendAuth = S::SpendAuth;
 }
 
@@ -488,7 +489,7 @@ impl MaybeSigned {
     }
 }
 
-impl<P, V> Bundle<InProgress<P, Unauthorized>, V> {
+impl<P: fmt::Debug, V> Bundle<InProgress<P, Unauthorized>, V> {
     /// Loads the sighash into this bundle, preparing it for signing.
     ///
     /// This API ensures that all signatures are created over the same sighash.
@@ -534,7 +535,7 @@ impl<V> Bundle<InProgress<Proof, Unauthorized>, V> {
     }
 }
 
-impl<P, V> Bundle<InProgress<P, PartiallyAuthorized>, V> {
+impl<P: fmt::Debug, V> Bundle<InProgress<P, PartiallyAuthorized>, V> {
     /// Signs this bundle with the given [`SpendAuthorizingKey`].
     ///
     /// This will apply signatures for all notes controlled by this spending key.
@@ -679,9 +680,9 @@ pub mod testing {
             for note in notes.iter() {
                 let leaf = MerkleHashOrchard::from_cmx(&note.commitment().into());
                 tree.append(&leaf);
-                tree.witness();
+                let (position, leaf) = tree.witness().expect("tree is not empty");
 
-                let path = tree.authentication_path(&leaf).unwrap().into();
+                let path = MerklePath::from((position, tree.authentication_path(position, &leaf).expect("we just witnessed the path")));
                 notes_and_auth_paths.push((*note, path));
             }
 
diff --git a/src/bundle.rs b/src/bundle.rs
index 4c0454c0..8f6de3d5 100644
--- a/src/bundle.rs
+++ b/src/bundle.rs
@@ -3,6 +3,7 @@
 pub mod commitments;
 
 use std::convert::TryInto;
+use std::fmt;
 use std::io;
 
 use blake2b_simd::Hash as Blake2bHash;
@@ -230,9 +231,9 @@ impl Flags {
 }
 
 /// Defines the authorization type of an Orchard bundle.
-pub trait Authorization {
+pub trait Authorization: fmt::Debug {
     /// The authorization type of an Orchard action.
-    type SpendAuth;
+    type SpendAuth: fmt::Debug;
 }
 
 /// A bundle of actions to be applied to the ledger.
diff --git a/src/keys.rs b/src/keys.rs
index 698e2010..3e135c22 100644
--- a/src/keys.rs
+++ b/src/keys.rs
@@ -407,12 +407,12 @@ impl FullViewingKey {
     /// Derives an internal full viewing key from a full viewing key, as specified in [ZIP32][orchardinternalfullviewingkey]
     ///
     /// [orchardinternalfullviewingkey]: https://zips.z.cash/zip-0032#orchard-internal-key-derivation
-    pub fn derive_internal(&self) -> Option<Self> {
-        Some(FullViewingKey {
+    pub fn derive_internal(&self) -> Self {
+        FullViewingKey {
             ak: self.ak.clone(),
             nk: self.nk,
             rivk: self.rivk_internal(),
-        })
+        }
     }
 }
 
@@ -981,7 +981,7 @@ mod tests {
             let internal_rivk = fvk.rivk_internal();
             assert_eq!(internal_rivk.0.to_repr(), tv.internal_rivk);
 
-            let internal_fvk = fvk.derive_internal().unwrap();
+            let internal_fvk = fvk.derive_internal();
             assert_eq!(internal_rivk, *internal_fvk.rivk());
 
             let internal_ivk: KeyAgreementPrivateKey = (&internal_fvk).into();
diff --git a/src/lib.rs b/src/lib.rs
index d0078466..b3579899 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -11,7 +11,7 @@
 // Temporary until we have more of the crate implemented.
 #![allow(dead_code)]
 // Catch documentation errors caused by code changes.
-#![deny(broken_intra_doc_links)]
+#![deny(rustdoc::broken_intra_doc_links)]
 #![deny(missing_debug_implementations)]
 #![deny(missing_docs)]
 #![deny(unsafe_code)]
diff --git a/src/note/nullifier.rs b/src/note/nullifier.rs
index db2c583d..17b9d5c3 100644
--- a/src/note/nullifier.rs
+++ b/src/note/nullifier.rs
@@ -11,7 +11,7 @@ use crate::{
 };
 
 /// A unique nullifier for a note.
-#[derive(Clone, Copy, Debug)]
+#[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord)]
 pub struct Nullifier(pub(crate) pallas::Base);
 
 impl Nullifier {
diff --git a/src/tree.rs b/src/tree.rs
index 729529f1..874d08e0 100644
--- a/src/tree.rs
+++ b/src/tree.rs
@@ -19,7 +19,7 @@ use serde::de::{Deserializer, Error};
 use serde::ser::Serializer;
 use serde::{Deserialize, Serialize};
 use std::iter;
-use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
+use subtle::{Choice, ConditionallySelectable, CtOption};
 
 // The uncommitted leaf is defined as pallas::Base(2).
 // <https://zips.z.cash/protocol/protocol.pdf#thmuncommittedorchard>
@@ -160,7 +160,7 @@ impl MerklePath {
 
 /// A newtype wrapper for leaves and internal nodes in the Orchard
 /// incremental note commitment tree.
-#[derive(Copy, Clone, Debug)]
+#[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord)]
 pub struct MerkleHashOrchard(pallas::Base);
 
 impl MerkleHashOrchard {
@@ -190,25 +190,6 @@ impl MerkleHashOrchard {
     }
 }
 
-/// This instance should only be used for hash table key comparisons.
-impl std::cmp::PartialEq for MerkleHashOrchard {
-    fn eq(&self, other: &Self) -> bool {
-        self.0.ct_eq(&other.0).into()
-    }
-}
-
-/// This instance should only be used for hash table key comparisons.
-impl std::cmp::Eq for MerkleHashOrchard {}
-
-/// This instance should only be used for hash table key hashing.
-impl std::hash::Hash for MerkleHashOrchard {
-    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
-        <Option<pallas::Base>>::from(self.0)
-            .map(|b| b.to_repr())
-            .hash(state)
-    }
-}
-
 impl ConditionallySelectable for MerkleHashOrchard {
     fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
         MerkleHashOrchard(pallas::Base::conditional_select(&a.0, &b.0, choice))
@@ -302,7 +283,7 @@ pub mod testing {
         {
             let cmx = MerkleHashOrchard::from_bytes(&tv.leaves[i]).unwrap();
             tree.append(&cmx);
-            tree.witness();
+            tree.witness().expect("tree is not empty");
 
             assert_eq!(tree.root().0, pallas::Base::from_repr(tv.root).unwrap());
 
@@ -312,14 +293,13 @@ pub mod testing {
             for j in 0..=i {
                 let leaf = MerkleHashOrchard::from_bytes(&tv.leaves[j]).unwrap();
                 assert_eq!(
-                    tree.authentication_path(&leaf),
-                    Some((
-                        j.try_into().unwrap(),
+                    tree.authentication_path(j.try_into().unwrap(), &leaf),
+                    Some(
                         tv.paths[j]
                             .iter()
                             .map(|v| MerkleHashOrchard::from_bytes(v).unwrap())
                             .collect()
-                    ))
+                    )
                 );
             }
         }
diff --git a/tests/builder.rs b/tests/builder.rs
index 41bce9fc..11d1d1b9 100644
--- a/tests/builder.rs
+++ b/tests/builder.rs
@@ -74,8 +74,8 @@ fn bundle_chain() {
         let leaf = MerkleHashOrchard::from_cmx(&cmx);
         let mut tree = BridgeTree::<MerkleHashOrchard, 32>::new(0);
         tree.append(&leaf);
-        tree.witness();
-        let (position, auth_path) = tree.authentication_path(&leaf).unwrap();
+        let (position, leaf) = tree.witness().unwrap();
+        let auth_path = tree.authentication_path(position, &leaf).unwrap();
         let merkle_path = MerklePath::from_parts(
             u64::from(position).try_into().unwrap(),
             auth_path[..].try_into().unwrap(),