diff --git a/zebra-network/src/peer/connection.rs b/zebra-network/src/peer/connection.rs
index abe17f11..2569aa2d 100644
--- a/zebra-network/src/peer/connection.rs
+++ b/zebra-network/src/peer/connection.rs
@@ -46,7 +46,8 @@ use super::{ClientRequest, ErrorSlot, PeerError, SharedPeerError};
 
 pub(super) enum Handler {
     /// Indicates that the handler has finished processing the request.
-    Finished(Result<Response, SharedPeerError>),
+    /// An error here is scoped to the request.
+    Finished(Result<Response, PeerError>),
     Ping(Nonce),
     Peers,
     FindBlocks,
@@ -66,17 +67,21 @@ impl Handler {
     /// Try to handle `msg` as a response to a client request, possibly consuming
     /// it in the process.
     ///
+    /// This function is where we statefully interpret Bitcoin/Zcash messages
+    /// into responses to messages in the internal request/response protocol.
+    /// This conversion is done by a sequence of (request, message) match arms,
+    /// each of which contains the conversion logic for that pair.
+    ///
     /// Taking ownership of the message means that we can pass ownership of its
     /// contents to responses without additional copies.  If the message is not
     /// interpretable as a response, we return ownership to the caller.
+    ///
+    /// Unexpected messages are left unprocessed, and may be rejected later.
     fn process_message(&mut self, msg: Message) -> Option<Message> {
-        // This function is where we statefully interpret Bitcoin/Zcash messages
-        // into responses to messages in the internal request/response protocol.
-        // This conversion is done by a sequence of (request, message) match arms,
-        // each of which contains the conversion logic for that pair.
         let mut ignored_msg = None;
         // XXX can this be avoided?
         let tmp_state = std::mem::replace(self, Handler::Finished(Ok(Response::Nil)));
+
         *self = match (tmp_state, msg) {
             (Handler::Ping(req_nonce), Message::Pong(rsp_nonce)) => {
                 if req_nonce == rsp_nonce {
@@ -95,19 +100,36 @@ impl Handler {
             ) => {
                 if hashes.remove(&transaction.hash()) {
                     transactions.push(transaction);
-                    if hashes.is_empty() {
-                        Handler::Finished(Ok(Response::Transactions(transactions)))
-                    } else {
-                        Handler::TransactionsByHash {
-                            hashes,
-                            transactions,
-                        }
-                    }
                 } else {
-                    // This transaction isn't the one we asked for,
-                    // but unsolicited transactions are OK, so leave
-                    // for future handling.
                     ignored_msg = Some(Message::Tx(transaction));
+                }
+                if hashes.is_empty() {
+                    Handler::Finished(Ok(Response::Transactions(transactions)))
+                } else {
+                    Handler::TransactionsByHash {
+                        hashes,
+                        transactions,
+                    }
+                }
+            }
+            (
+                Handler::TransactionsByHash {
+                    hashes,
+                    transactions,
+                },
+                Message::NotFound(items),
+            ) => {
+                let hash_in_hashes = |item: &InventoryHash| {
+                    if let InventoryHash::Tx(hash) = item {
+                        hashes.contains(hash)
+                    } else {
+                        false
+                    }
+                };
+                if items.iter().all(hash_in_hashes) {
+                    Handler::Finished(Err(PeerError::NotFound(items)))
+                } else {
+                    ignored_msg = Some(Message::NotFound(items));
                     Handler::TransactionsByHash {
                         hashes,
                         transactions,
@@ -123,15 +145,28 @@ impl Handler {
             ) => {
                 if hashes.remove(&block.hash()) {
                     blocks.push(block);
-                    if hashes.is_empty() {
-                        Handler::Finished(Ok(Response::Blocks(blocks)))
-                    } else {
-                        Handler::BlocksByHash { hashes, blocks }
-                    }
                 } else {
-                    // Blocks shouldn't be sent unsolicited,
-                    // so fail the request if we got the wrong one.
-                    Handler::Finished(Err(PeerError::WrongBlock.into()))
+                    ignored_msg = Some(Message::Block(block));
+                }
+                if hashes.is_empty() {
+                    Handler::Finished(Ok(Response::Blocks(blocks)))
+                } else {
+                    Handler::BlocksByHash { hashes, blocks }
+                }
+            }
+            (Handler::BlocksByHash { hashes, blocks }, Message::NotFound(items)) => {
+                let hash_in_hashes = |item: &InventoryHash| {
+                    if let InventoryHash::Block(hash) = item {
+                        hashes.contains(hash)
+                    } else {
+                        false
+                    }
+                };
+                if items.iter().all(hash_in_hashes) {
+                    Handler::Finished(Err(PeerError::NotFound(items)))
+                } else {
+                    ignored_msg = Some(Message::NotFound(items));
+                    Handler::BlocksByHash { hashes, blocks }
                 }
             }
             (Handler::FindBlocks, Message::Inv(items))
@@ -292,7 +327,7 @@ where
                                         tx,
                                         ..
                                     } => {
-                                        let _ = tx.send(response);
+                                        let _ = tx.send(response.map_err(Into::into));
                                         State::AwaitingRequest
                                     }
                                     pending @ State::AwaitingResponse { .. } => pending,
diff --git a/zebra-network/src/peer/error.rs b/zebra-network/src/peer/error.rs
index 5398eb7e..2fd3df98 100644
--- a/zebra-network/src/peer/error.rs
+++ b/zebra-network/src/peer/error.rs
@@ -5,6 +5,8 @@ use thiserror::Error;
 use tracing_error::TracedError;
 use zebra_chain::serialization::SerializationError;
 
+use crate::protocol::external::InventoryHash;
+
 /// A wrapper around `Arc<PeerError>` that implements `Error`.
 #[derive(Error, Debug, Clone)]
 #[error(transparent)]
@@ -57,6 +59,9 @@ pub enum PeerError {
     /// The remote peer responded with a block we didn't ask for.
     #[error("Remote peer responded with a block we didn't ask for.")]
     WrongBlock,
+    /// We requested data that the peer couldn't find.
+    #[error("Remote peer could not find items: {0:?}")]
+    NotFound(Vec<InventoryHash>),
 }
 
 #[derive(Default, Clone)]