diff --git a/digest/CHANGELOG.md b/digest/CHANGELOG.md
index 8af2a4d3..237e7887 100644
--- a/digest/CHANGELOG.md
+++ b/digest/CHANGELOG.md
@@ -16,12 +16,15 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ### Removed
 - `Mac::new`, `Mac::new_from_slice`, and `Mac::generate_key` methods ([#1173])
 - `HashReader` and `HashWriter` are moved to the `digest-io` crate ([#1809])
-- Removed `io::Write/Read` implementations in favor of the `digest_io::IoWrapper` type ([#1809])
+- `io::Write/Read` implementations in favor of the `digest_io::IoWrapper` type ([#1809])
+- `AssociatedOid` blanket impls for `CoreWrapper` and `CtVariableCoreWrapper` ([#1810])
+- `impl_oid_carrier!` macro ([#1810])
 
 [#1173]: https://github.com/RustCrypto/traits/pull/1173
 [#1334]: https://github.com/RustCrypto/traits/pull/1334
 [#1759]: https://github.com/RustCrypto/traits/pull/1759
 [#1809]: https://github.com/RustCrypto/traits/pull/1809
+[#1810]: https://github.com/RustCrypto/traits/pull/1810
 
 ## 0.10.7 (2023-05-19)
 ### Changed
diff --git a/digest/src/core_api/ct_variable.rs b/digest/src/core_api/ct_variable.rs
index 983f610c..eeb9cd55 100644
--- a/digest/src/core_api/ct_variable.rs
+++ b/digest/src/core_api/ct_variable.rs
@@ -5,8 +5,6 @@ use super::{
 #[cfg(feature = "mac")]
 use crate::MacMarker;
 use crate::{CustomizedInit, HashMarker, VarOutputCustomized};
-#[cfg(feature = "oid")]
-use const_oid::{AssociatedOid, ObjectIdentifier};
 use core::{
     fmt,
     marker::PhantomData,
@@ -18,26 +16,20 @@ use crypto_common::{
     hazmat::{DeserializeStateError, SerializableState, SerializedState, SubSerializedStateSize},
     typenum::{IsLess, IsLessOrEqual, Le, LeEq, NonZero, Sum, U1, U256},
 };
-
-/// Dummy type used with [`CtVariableCoreWrapper`] in cases when
-/// resulting hash does not have a known OID.
-#[derive(Copy, Clone, Debug, Eq, PartialEq, Hash)]
-pub struct NoOid;
-
 /// Wrapper around [`VariableOutputCore`] which selects output size
 /// at compile time.
 #[derive(Clone)]
-pub struct CtVariableCoreWrapper<T, OutSize, O = NoOid>
+pub struct CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
     LeEq<OutSize, T::OutputSize>: NonZero,
 {
     inner: T,
-    _out: PhantomData<(OutSize, O)>,
+    _out: PhantomData<OutSize>,
 }
 
-impl<T, OutSize, O> HashMarker for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> HashMarker for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore + HashMarker,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -46,7 +38,7 @@ where
 }
 
 #[cfg(feature = "mac")]
-impl<T, OutSize, O> MacMarker for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> MacMarker for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore + MacMarker,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -54,7 +46,7 @@ where
 {
 }
 
-impl<T, OutSize, O> BlockSizeUser for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> BlockSizeUser for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -63,7 +55,7 @@ where
     type BlockSize = T::BlockSize;
 }
 
-impl<T, OutSize, O> UpdateCore for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> UpdateCore for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -75,7 +67,7 @@ where
     }
 }
 
-impl<T, OutSize, O> OutputSizeUser for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> OutputSizeUser for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -84,7 +76,7 @@ where
     type OutputSize = OutSize;
 }
 
-impl<T, OutSize, O> BufferKindUser for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> BufferKindUser for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -93,7 +85,7 @@ where
     type BufferKind = T::BufferKind;
 }
 
-impl<T, OutSize, O> FixedOutputCore for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> FixedOutputCore for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -116,7 +108,7 @@ where
     }
 }
 
-impl<T, OutSize, O> Default for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> Default for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -131,7 +123,7 @@ where
     }
 }
 
-impl<T, OutSize, O> CustomizedInit for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> CustomizedInit for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore + VarOutputCustomized,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -146,7 +138,7 @@ where
     }
 }
 
-impl<T, OutSize, O> Reset for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> Reset for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -158,7 +150,7 @@ where
     }
 }
 
-impl<T, OutSize, O> AlgorithmName for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> AlgorithmName for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore + AlgorithmName,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -171,19 +163,8 @@ where
     }
 }
 
-#[cfg(feature = "oid")]
-impl<T, OutSize, O> AssociatedOid for CtVariableCoreWrapper<T, OutSize, O>
-where
-    T: VariableOutputCore,
-    O: AssociatedOid,
-    OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
-    LeEq<OutSize, T::OutputSize>: NonZero,
-{
-    const OID: ObjectIdentifier = O::OID;
-}
-
 #[cfg(feature = "zeroize")]
-impl<T, OutSize, O> zeroize::ZeroizeOnDrop for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> zeroize::ZeroizeOnDrop for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore + zeroize::ZeroizeOnDrop,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -191,7 +172,7 @@ where
 {
 }
 
-impl<T, OutSize, O> fmt::Debug for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> fmt::Debug for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore + AlgorithmName,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
@@ -202,26 +183,10 @@ where
     }
 }
 
-/// Implement dummy type with hidden docs which is used to "carry" hasher
-/// OID for [`CtVariableCoreWrapper`].
-#[macro_export]
-macro_rules! impl_oid_carrier {
-    ($name:ident, $oid:literal) => {
-        #[doc(hidden)]
-        #[derive(Copy, Clone, Debug, Eq, PartialEq, Hash)]
-        pub struct $name;
-
-        #[cfg(feature = "oid")]
-        impl AssociatedOid for $name {
-            const OID: ObjectIdentifier = ObjectIdentifier::new_unwrap($oid);
-        }
-    };
-}
-
 type CtVariableCoreWrapperSerializedStateSize<T> =
     Sum<<T as SerializableState>::SerializedStateSize, U1>;
 
-impl<T, OutSize, O> SerializableState for CtVariableCoreWrapper<T, OutSize, O>
+impl<T, OutSize> SerializableState for CtVariableCoreWrapper<T, OutSize>
 where
     T: VariableOutputCore + SerializableState,
     OutSize: ArraySize + IsLessOrEqual<T::OutputSize>,
diff --git a/digest/src/core_api/wrapper.rs b/digest/src/core_api/wrapper.rs
index 8d4cf641..6cd006fa 100644
--- a/digest/src/core_api/wrapper.rs
+++ b/digest/src/core_api/wrapper.rs
@@ -21,8 +21,6 @@ use crypto_common::{
 
 #[cfg(feature = "mac")]
 use crate::MacMarker;
-#[cfg(feature = "oid")]
-use const_oid::{AssociatedOid, ObjectIdentifier};
 
 /// Wrapper around [`BufferKindUser`].
 ///
@@ -171,14 +169,6 @@ where
     }
 }
 
-#[cfg(feature = "oid")]
-impl<T> AssociatedOid for CoreWrapper<T>
-where
-    T: BufferKindUser + AssociatedOid,
-{
-    const OID: ObjectIdentifier = T::OID;
-}
-
 type CoreWrapperSerializedStateSize<T> =
     Sum<Sum<<T as SerializableState>::SerializedStateSize, U1>, <T as BlockSizeUser>::BlockSize>;
 
diff --git a/digest/src/digest.rs b/digest/src/digest.rs
index 1de1ea86..ef084928 100644
--- a/digest/src/digest.rs
+++ b/digest/src/digest.rs
@@ -3,7 +3,7 @@ use crypto_common::{Output, OutputSizeUser, typenum::Unsigned};
 
 #[cfg(feature = "alloc")]
 use alloc::boxed::Box;
-#[cfg(feature = "const-oid")]
+#[cfg(feature = "oid")]
 use const_oid::DynAssociatedOid;
 
 /// Marker trait for cryptographic hash functions.
@@ -228,8 +228,8 @@ impl Clone for Box<dyn DynDigest> {
 }
 
 /// Convenience wrapper trait around [DynDigest] and [DynAssociatedOid].
-#[cfg(feature = "const-oid")]
+#[cfg(feature = "oid")]
 pub trait DynDigestWithOid: DynDigest + DynAssociatedOid {}
 
-#[cfg(feature = "const-oid")]
+#[cfg(feature = "oid")]
 impl<T: DynDigest + DynAssociatedOid> DynDigestWithOid for T {}
diff --git a/digest/src/lib.rs b/digest/src/lib.rs
index e323f364..b0febdf1 100644
--- a/digest/src/lib.rs
+++ b/digest/src/lib.rs
@@ -62,7 +62,7 @@ pub use block_buffer;
 pub use const_oid;
 pub use crypto_common;
 
-#[cfg(feature = "const-oid")]
+#[cfg(feature = "oid")]
 pub use crate::digest::DynDigestWithOid;
 pub use crate::digest::{Digest, DynDigest, HashMarker};
 #[cfg(feature = "mac")]