diff --git a/hashes/Cargo.toml b/hashes/Cargo.toml
index 404fbb4a3..54bd229a7 100644
--- a/hashes/Cargo.toml
+++ b/hashes/Cargo.toml
@@ -17,6 +17,7 @@ exclude = ["tests", "contrib"]
 default = ["std"]
 std = ["alloc", "hex/std", "bitcoin-io/std"]
 alloc = ["hex/alloc"]
+schemars = ["dep:schemars", "alloc"]
 # If you want I/O you must enable either "std" or "io".
 io = ["bitcoin-io"]
 # Smaller (but slower) implementation of sha256, sha512 and ripemd160
diff --git a/hashes/src/hash160.rs b/hashes/src/hash160.rs
index b59d0379b..ba4d4724e 100644
--- a/hashes/src/hash160.rs
+++ b/hashes/src/hash160.rs
@@ -51,6 +51,8 @@ mod tests {
     #[test]
     #[cfg(feature = "alloc")]
     fn test() {
+        use alloc::string::ToString;
+
         use super::Hash;
         use crate::{hash160, HashEngine};
 
diff --git a/hashes/src/hkdf.rs b/hashes/src/hkdf.rs
index 1de1cd616..452c46a58 100644
--- a/hashes/src/hkdf.rs
+++ b/hashes/src/hkdf.rs
@@ -5,9 +5,9 @@
 //! Implementation based on RFC5869, but the interface is scoped
 //! to BIP324's requirements.
 
-#[cfg(all(feature = "alloc", not(feature = "std")))]
+#[cfg(feature = "alloc")]
 use alloc::vec;
-#[cfg(all(feature = "alloc", not(feature = "std")))]
+#[cfg(feature = "alloc")]
 use alloc::vec::Vec;
 use core::fmt;
 
diff --git a/hashes/src/hmac.rs b/hashes/src/hmac.rs
index 4a90cc043..ce501a505 100644
--- a/hashes/src/hmac.rs
+++ b/hashes/src/hmac.rs
@@ -23,7 +23,7 @@ pub struct Hmac<T: GeneralHash>(T);
 impl<T: GeneralHash + schemars::JsonSchema> schemars::JsonSchema for Hmac<T> {
     fn is_referenceable() -> bool { <T as schemars::JsonSchema>::is_referenceable() }
 
-    fn schema_name() -> std::string::String { <T as schemars::JsonSchema>::schema_name() }
+    fn schema_name() -> alloc::string::String { <T as schemars::JsonSchema>::schema_name() }
 
     fn json_schema(gen: &mut schemars::gen::SchemaGenerator) -> schemars::schema::Schema {
         <T as schemars::JsonSchema>::json_schema(gen)
diff --git a/hashes/src/impls.rs b/hashes/src/impls.rs
index 09f46496f..2e69309c8 100644
--- a/hashes/src/impls.rs
+++ b/hashes/src/impls.rs
@@ -81,8 +81,10 @@ impl_write!(
     T: crate::GeneralHash
 );
 
-#[cfg(test)]
+#[cfg(all(test, feature = "alloc"))] // right now every test here depends on `alloc`
 mod tests {
+    use alloc::format;
+
     use bitcoin_io::Write;
 
     use crate::{
diff --git a/hashes/src/internal_macros.rs b/hashes/src/internal_macros.rs
index a105a66c3..acae8df6d 100644
--- a/hashes/src/internal_macros.rs
+++ b/hashes/src/internal_macros.rs
@@ -224,9 +224,17 @@ macro_rules! hash_type_no_default {
 
         #[cfg(feature = "schemars")]
         impl schemars::JsonSchema for Hash {
-            fn schema_name() -> String { "Hash".to_owned() }
+            fn schema_name() -> alloc::string::String {
+                use alloc::borrow::ToOwned;
+
+                "Hash".to_owned()
+            }
 
             fn json_schema(gen: &mut schemars::gen::SchemaGenerator) -> schemars::schema::Schema {
+                use alloc::borrow::ToOwned;
+                use alloc::boxed::Box;
+                use alloc::string::String;
+
                 let len = $bits / 8;
                 let mut schema: schemars::schema::SchemaObject = <String>::json_schema(gen).into();
                 schema.string = Some(Box::new(schemars::schema::StringValidation {
diff --git a/hashes/src/lib.rs b/hashes/src/lib.rs
index 897f97b8f..0eadb86e7 100644
--- a/hashes/src/lib.rs
+++ b/hashes/src/lib.rs
@@ -62,7 +62,7 @@
 //! # fn main() {}
 //! ```
 
-#![cfg_attr(all(not(test), not(feature = "std")), no_std)]
+#![cfg_attr(not(feature = "std"), no_std)]
 // Experimental features we need.
 #![cfg_attr(docsrs, feature(doc_auto_cfg))]
 #![cfg_attr(bench, feature(test))]
@@ -75,9 +75,9 @@
 #![allow(clippy::manual_range_contains)] // More readable than clippy's format.
 #![allow(clippy::needless_borrows_for_generic_args)] // https://github.com/rust-lang/rust-clippy/issues/12454
 
-#[cfg(all(feature = "alloc", not(feature = "std")))]
+#[cfg(feature = "alloc")]
 extern crate alloc;
-#[cfg(any(test, feature = "std"))]
+
 extern crate core;
 
 #[cfg(feature = "bitcoin-io")]
@@ -334,16 +334,19 @@ mod tests {
         struct TestNewtype2(sha256d::Hash);
     }
 
-    #[rustfmt::skip]
-    const DUMMY: TestNewtype = TestNewtype::from_byte_array([
-        0x12, 0x23, 0x34, 0x45, 0x56, 0x67, 0x78, 0x89,
-        0x13, 0x24, 0x35, 0x46, 0x57, 0x68, 0x79, 0x8a,
-        0x14, 0x25, 0x36, 0x47, 0x58, 0x69, 0x7a, 0x8b,
-        0x15, 0x26, 0x37, 0x48, 0x59, 0x6a, 0x7b, 0x8c,
-    ]);
-
     #[test]
+    #[cfg(feature = "alloc")]
     fn newtype_fmt_roundtrip() {
+        use alloc::format;
+
+        #[rustfmt::skip]
+        const DUMMY: TestNewtype = TestNewtype::from_byte_array([
+            0x12, 0x23, 0x34, 0x45, 0x56, 0x67, 0x78, 0x89,
+            0x13, 0x24, 0x35, 0x46, 0x57, 0x68, 0x79, 0x8a,
+            0x14, 0x25, 0x36, 0x47, 0x58, 0x69, 0x7a, 0x8b,
+            0x15, 0x26, 0x37, 0x48, 0x59, 0x6a, 0x7b, 0x8c,
+        ]);
+
         let orig = DUMMY;
         let hex = format!("{}", orig);
         let rinsed = hex.parse::<TestNewtype>().expect("failed to parse hex");
diff --git a/hashes/src/ripemd160.rs b/hashes/src/ripemd160.rs
index 3935ea25f..13a1248d4 100644
--- a/hashes/src/ripemd160.rs
+++ b/hashes/src/ripemd160.rs
@@ -413,6 +413,8 @@ mod tests {
     #[test]
     #[cfg(feature = "alloc")]
     fn test() {
+        use alloc::string::ToString;
+
         use crate::{ripemd160, HashEngine};
 
         #[derive(Clone)]
diff --git a/hashes/src/sha1.rs b/hashes/src/sha1.rs
index ea9ce848f..7ca56f0c1 100644
--- a/hashes/src/sha1.rs
+++ b/hashes/src/sha1.rs
@@ -132,6 +132,8 @@ mod tests {
     #[test]
     #[cfg(feature = "alloc")]
     fn test() {
+        use alloc::string::ToString;
+
         use crate::{sha1, HashEngine};
 
         #[derive(Clone)]
diff --git a/hashes/src/sha256.rs b/hashes/src/sha256.rs
index 0e23142e7..d7377a212 100644
--- a/hashes/src/sha256.rs
+++ b/hashes/src/sha256.rs
@@ -864,12 +864,16 @@ impl HashEngine {
 
 #[cfg(test)]
 mod tests {
+    use core::array;
+
     use super::*;
     use crate::{sha256, HashEngine};
 
     #[test]
     #[cfg(feature = "alloc")]
     fn test() {
+        use alloc::string::ToString;
+
         #[derive(Clone)]
         struct Test {
             input: &'static str,
@@ -931,7 +935,10 @@ mod tests {
     }
 
     #[test]
+    #[cfg(feature = "alloc")]
     fn fmt_roundtrips() {
+        use alloc::format;
+
         let hash = sha256::Hash::hash(b"some arbitrary bytes");
         let hex = format!("{}", hash);
         let rinsed = hex.parse::<sha256::Hash>().expect("failed to parse hex");
@@ -1023,14 +1030,13 @@ mod tests {
 
     #[test]
     fn hash_unoptimized() {
-        assert_eq!(Hash::hash(&[]), Hash::hash_unoptimized(&[]));
+        let bytes: [u8; 256] = array::from_fn(|i| i as u8);
 
-        let mut bytes = Vec::new();
-        for i in 0..256 {
-            bytes.push(i as u8);
+        for i in 0..=256 {
+            let bytes = &bytes[0..i];
             assert_eq!(
-                Hash::hash(&bytes),
-                Hash::hash_unoptimized(&bytes),
+                Hash::hash(bytes),
+                Hash::hash_unoptimized(bytes),
                 "hashes don't match for length {}",
                 i + 1
             );
@@ -1050,7 +1056,10 @@ mod tests {
     fn const_midstate() { assert_eq!(Midstate::hash_tag(b"TapLeaf"), TAP_LEAF_MIDSTATE,) }
 
     #[test]
+    #[cfg(feature = "alloc")]
     fn regression_midstate_debug_format() {
+        use alloc::format;
+
         let want = "Midstate { bytes: 9ce0e4e67c116c3938b3caf2c30f5089d3f3936c47636e607db33eeaddc6f0c9, length: 64 }";
         let got = format!("{:?}", TAP_LEAF_MIDSTATE);
         assert_eq!(got, want);
diff --git a/hashes/src/sha256d.rs b/hashes/src/sha256d.rs
index f0be7c0de..72f246887 100644
--- a/hashes/src/sha256d.rs
+++ b/hashes/src/sha256d.rs
@@ -43,11 +43,14 @@ fn from_engine(e: HashEngine) -> Hash {
 
 #[cfg(test)]
 mod tests {
+    #[allow(unused_imports)] // whether this is used depends on features
     use crate::sha256d;
 
     #[test]
     #[cfg(feature = "alloc")]
     fn test() {
+        use alloc::string::ToString;
+
         use crate::{sha256, HashEngine};
 
         #[derive(Clone)]
@@ -97,7 +100,10 @@ mod tests {
     }
 
     #[test]
+    #[cfg(feature = "alloc")]
     fn fmt_roundtrips() {
+        use alloc::format;
+
         let hash = sha256d::Hash::hash(b"some arbitrary bytes");
         let hex = format!("{}", hash);
         let rinsed = hex.parse::<sha256d::Hash>().expect("failed to parse hex");
diff --git a/hashes/src/sha256t.rs b/hashes/src/sha256t.rs
index 6061e743c..655e58783 100644
--- a/hashes/src/sha256t.rs
+++ b/hashes/src/sha256t.rs
@@ -23,9 +23,17 @@ pub struct Hash<T>([u8; 32], PhantomData<T>);
 
 #[cfg(feature = "schemars")]
 impl<T: Tag> schemars::JsonSchema for Hash<T> {
-    fn schema_name() -> String { "Hash".to_owned() }
+    fn schema_name() -> alloc::string::String {
+        use alloc::borrow::ToOwned;
+
+        "Hash".to_owned()
+    }
 
     fn json_schema(gen: &mut schemars::gen::SchemaGenerator) -> schemars::schema::Schema {
+        use alloc::borrow::ToOwned;
+        use alloc::boxed::Box;
+        use alloc::string::String;
+
         let mut schema: schemars::schema::SchemaObject = <String>::json_schema(gen).into();
         schema.string = Some(Box::new(schemars::schema::StringValidation {
             max_length: Some(32 * 2),
@@ -353,6 +361,8 @@ mod tests {
     #[test]
     #[cfg(feature = "alloc")]
     fn manually_created_sha256t_hash_type() {
+        use alloc::string::ToString;
+
         assert_eq!(TestHash::hash(&[0]).to_string(), HASH_ZERO_FORWARD);
     }
 
@@ -370,6 +380,8 @@ mod tests {
     #[test]
     #[cfg(feature = "alloc")]
     fn macro_created_sha256t_hash_type_backward() {
+        use alloc::string::ToString;
+
         let inner = sha256t::Hash::<NewTypeTagBackward>::hash(&[0]);
         let hash = NewTypeHashBackward::from_byte_array(inner.to_byte_array());
         assert_eq!(hash.to_string(), HASH_ZERO_BACKWARD);
@@ -391,6 +403,8 @@ mod tests {
     #[test]
     #[cfg(feature = "alloc")]
     fn macro_created_sha256t_hash_type_prints_forward() {
+        use alloc::string::ToString;
+
         let inner = sha256t::Hash::<NewTypeTagForward>::hash(&[0]);
         let hash = NewTypeHashForward::from_byte_array(inner.to_byte_array());
         assert_eq!(hash.to_string(), HASH_ZERO_FORWARD);
diff --git a/hashes/src/sha384.rs b/hashes/src/sha384.rs
index 2531624ed..c588309cb 100644
--- a/hashes/src/sha384.rs
+++ b/hashes/src/sha384.rs
@@ -45,6 +45,8 @@ mod tests {
     #[test]
     #[cfg(feature = "alloc")]
     fn test() {
+        use alloc::string::ToString;
+
         use crate::{sha384, HashEngine};
 
         #[derive(Clone)]
diff --git a/hashes/src/sha512.rs b/hashes/src/sha512.rs
index 689691b89..4a4df0617 100644
--- a/hashes/src/sha512.rs
+++ b/hashes/src/sha512.rs
@@ -310,6 +310,8 @@ mod tests {
     #[test]
     #[cfg(feature = "alloc")]
     fn test() {
+        use alloc::string::ToString;
+
         use crate::{sha512, HashEngine};
 
         #[derive(Clone)]
diff --git a/hashes/src/sha512_256.rs b/hashes/src/sha512_256.rs
index 3c303c8c2..30b36e82b 100644
--- a/hashes/src/sha512_256.rs
+++ b/hashes/src/sha512_256.rs
@@ -55,6 +55,8 @@ mod tests {
     #[test]
     #[cfg(feature = "alloc")]
     fn test() {
+        use alloc::string::ToString;
+
         use crate::{sha512_256, HashEngine};
 
         #[derive(Clone)]
diff --git a/hashes/src/util.rs b/hashes/src/util.rs
index 58d08d9f1..17a2dc8f2 100644
--- a/hashes/src/util.rs
+++ b/hashes/src/util.rs
@@ -400,28 +400,40 @@ mod test {
     }
 
     #[test]
+    #[cfg(feature = "alloc")]
     fn display() {
+        use alloc::format;
+
         let want = "0000000000000000000000000000000000000000000000000000000000000000";
         let got = format!("{}", TestHash::all_zeros());
         assert_eq!(got, want)
     }
 
     #[test]
+    #[cfg(feature = "alloc")]
     fn display_alternate() {
+        use alloc::format;
+
         let want = "0x0000000000000000000000000000000000000000000000000000000000000000";
         let got = format!("{:#}", TestHash::all_zeros());
         assert_eq!(got, want)
     }
 
     #[test]
+    #[cfg(feature = "alloc")]
     fn lower_hex() {
+        use alloc::format;
+
         let want = "0000000000000000000000000000000000000000000000000000000000000000";
         let got = format!("{:x}", TestHash::all_zeros());
         assert_eq!(got, want)
     }
 
     #[test]
+    #[cfg(feature = "alloc")]
     fn lower_hex_alternate() {
+        use alloc::format;
+
         let want = "0x0000000000000000000000000000000000000000000000000000000000000000";
         let got = format!("{:#x}", TestHash::all_zeros());
         assert_eq!(got, want)