docs: Remove varint from rustdoc

diff --git a/bitcoin/src/blockdata/transaction.rs b/bitcoin/src/blockdata/transaction.rs
index c017a06a..c964c4e2 100644
--- a/bitcoin/src/blockdata/transaction.rs
+++ b/bitcoin/src/blockdata/transaction.rs
@@ -119,8 +119,8 @@ internal_macros::define_extension_trait! {
         /// The weight of the TxIn when it's included in a SegWit transaction (i.e., a transaction
         /// having at least one SegWit input).
         ///
-        /// This always takes into account the witness, even when empty, in which
-        /// case 1WU for the witness length varint (`00`) is included.
+        /// This always takes into account the witness, even when empty (in which
+        /// case 1WU for the witness length `00` is included).
         ///
         /// Keep in mind that when adding a TxIn to a transaction, the total weight of the transaction
         /// might increase more than `TxIn::segwit_weight`. This happens when:
@@ -795,8 +795,7 @@ pub fn effective_value(
 ///   of the to-be-constructed transaction.
 ///
 /// Note that lengths of the scripts and witness elements must be non-serialized, IOW *without* the
-/// preceding compact size. The length of preceding compact size is computed and added inside the
-/// function for convenience.
+/// length prefix. The length is computed and added inside the function for convenience.
 ///
 /// If you have the transaction already constructed (except for signatures) with a dummy value for
 /// fee output you can use the return value of [`Transaction::script_pubkey_lens`] method directly
@@ -1116,7 +1115,7 @@ impl InputWeightPrediction {
     }
 
     /// Computes the **signature weight** added to a transaction by an input with this weight prediction,
-    /// not counting the prevout (txid, index), sequence, potential witness flag bytes or the witness count varint.
+    /// not counting the prevout (txid, index), sequence, potential witness flag bytes or the witness count.
     ///
     /// This function's internal arithmetic saturates at u32::MAX, so the return value of this
     /// function may be inaccurate for extremely large witness predictions.
@@ -1138,7 +1137,7 @@ impl InputWeightPrediction {
     }
 
     /// Computes the **signature weight** added to a transaction by an input with this weight prediction,
-    /// not counting the prevout (txid, index), sequence, potential witness flag bytes or the witness count varint.
+    /// not counting the prevout (txid, index), sequence, potential witness flag bytes or the witness count.
     ///
     /// This function's internal arithmetic saturates at u32::MAX, so the return value of this
     /// function may be inaccurate for extremely large witness predictions.
diff --git a/bitcoin/src/merkle_tree/block.rs b/bitcoin/src/merkle_tree/block.rs
index fe19904d..3629585f 100644
--- a/bitcoin/src/merkle_tree/block.rs
+++ b/bitcoin/src/merkle_tree/block.rs
@@ -163,11 +163,11 @@ impl Decodable for MerkleBlock {
 ///   N <= 1 + matched_transactions*tree_height
 ///
 /// The serialization format:
-///  - uint32     total_transactions (4 bytes)
-///  - varint     number of hashes   (1-3 bytes)
-///  - uint256[]  hashes in depth-first order (<= 32*N bytes)
-///  - varint     number of bytes of flag bits (1-3 bytes)
-///  - byte[]     flag bits, packed per 8 in a byte, least significant bit first (<= 2*N-1 bits)
+///  - uint32       total_transactions (4 bytes)
+///  - CompactSize  number of hashes   (1-3 bytes)
+///  - uint256[]    hashes in depth-first order (<= 32*N bytes)
+///  - CompactSize  number of bytes of flag bits (1-3 bytes)
+///  - byte[]       flag bits, packed per 8 in a byte, least significant bit first (<= 2*N-1 bits)
 ///
 /// The size constraints follow from this.
 #[derive(PartialEq, Eq, Clone, Debug)]
diff --git a/primitives/src/witness.rs b/primitives/src/witness.rs
index 02f9c7a7..098c5c64 100644
--- a/primitives/src/witness.rs
+++ b/primitives/src/witness.rs
@@ -31,12 +31,14 @@ use crate::prelude::{Box, Vec};
 pub struct Witness {
     /// Contains the witness `Vec<Vec<u8>>` serialization.
     ///
-    /// Does not include the initial varint indicating the number of elements. Each element however,
-    /// does include a varint indicating the element length. The number of elements is stored in
-    /// `witness_elements`.
+    /// Does not include the initial length prefix indicating the number of elements. Each element
+    /// however, does include a [`CompactSize`] indicating the element length. The number of
+    /// elements is stored in `witness_elements`.
     ///
     /// Concatenated onto the end of `content` is the index area. This is a `4 * witness_elements`
     /// bytes area which stores the index of the start of each witness item.
+    ///
+    /// [`CompactSize`]: <https://en.bitcoin.it/wiki/Protocol_documentation#Variable_length_integer>
     content: Vec<u8>,
 
     /// The number of elements in the witness.