diff --git a/zebra-state/src/service.rs b/zebra-state/src/service.rs
index e99d628af44..5310126aa78 100644
--- a/zebra-state/src/service.rs
+++ b/zebra-state/src/service.rs
@@ -530,13 +530,6 @@ impl Service<Request> for StateService {
     type Future =
         Pin<Box<dyn Future<Output = Result<Self::Response, Self::Error>> + Send + 'static>>;
 
-    // ## Correctness:
-    //
-    // This function must not return Poll::Pending, unless:
-    // 1. We remove all instances of `call_all` on the state service, or fix the leaked
-    //    service reservation in the `CallAll` implementation:
-    //    https://github.com/tower-rs/tower/blob/master/tower/src/util/call_all/common.rs#L112
-    // 2. We schedule the current task for wakeup via the `Context`
     fn poll_ready(&mut self, _: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
         let now = Instant::now();
 
diff --git a/zebrad/src/components/inbound.rs b/zebrad/src/components/inbound.rs
index 7041d66bc86..e40f4c73c44 100644
--- a/zebrad/src/components/inbound.rs
+++ b/zebrad/src/components/inbound.rs
@@ -7,7 +7,7 @@ use std::{
 
 use futures::{
     future::{FutureExt, TryFutureExt},
-    stream::{Stream, TryStreamExt},
+    stream::Stream,
 };
 use tokio::sync::oneshot;
 use tower::{buffer::Buffer, timeout::Timeout, util::BoxService, Service, ServiceExt};
@@ -52,12 +52,6 @@ pub type SetupData = (Outbound, Arc<Mutex<AddressBook>>);
 /// behind the current tip, while the `Inbound` service is *externally driven*,
 /// responding to block gossip by attempting to download and validate advertised
 /// blocks.
-///
-/// ## Correctness
-///
-/// The `state` service must not return `Poll::Pending`. If it does, a bug in the
-/// `ServiceExt::call_all` implementation might cause the `state` buffer to fill
-/// up, and make Zebra hang.
 pub struct Inbound {
     // invariants:
     //  * Before setup: address_book and downloads are None, and the *_setup members are Some
@@ -160,18 +154,14 @@ impl Service<zn::Request> for Inbound {
         }
 
         // TODO:
-        //  * do we want to propagate backpressure from the download queue or its outbound network here?
-        //    currently, the download queue waits for the outbound network in the download future, and
-        //    drops new requests after it reaches a hard-coded limit. This is the "load shed directly"
-        //    pattern from #1618.
-        //  * if we want to propagate backpressure, add a ReadyCache to ensure that each poll_ready
-        //    has a matching call. See #1593 for details.
-
-        // Ignore state readiness, to avoid reserving its buffer slots.
-        // We can't use a state ReadyCache, because call_all uses state directly.
-        // We can't call state.poll_ready, because:
-        //  * call_all also calls poll_ready
-        //  * some requests don't use the state
+        //  * do we want to propagate backpressure from the download queue or its outbound network?
+        //    currently, the download queue waits for the outbound network in the download future,
+        //    and drops new requests after it reaches a hard-coded limit. This is the
+        //    "load shed directly" pattern from #1618.
+        //  * currently, the state service is always ready, unless its buffer is full.
+        //    So we might also want to propagate backpressure from its buffer.
+        //  * if we want to propagate backpressure, add a ReadyCache for each service, to ensure
+        //    that each poll_ready has a matching call. See #1593 for details.
         Poll::Ready(Ok(()))
     }
 
@@ -194,34 +184,26 @@ impl Service<zn::Request> for Inbound {
             zn::Request::BlocksByHash(hashes) => {
                 // Correctness:
                 //
-                // We don't need to use ServiceExt::oneshot here, because
-                // call_all uses poll_ready internally.
-                //
-                // The state must not return Poll::Pending, because call_all
-                // leaks a buffer reservation every time that happens
+                // We can't use `call_all` here, because it leaks buffer slots:
                 // https://github.com/tower-rs/tower/blob/master/tower/src/util/call_all/common.rs#L112
-                let state = self.state.clone();
-                let requests = futures::stream::iter(
-                    hashes
-                        .into_iter()
-                        .map(|hash| zs::Request::Block(hash.into())),
-                );
-
-                state
-                    .call_all(requests)
-                    .try_filter_map(|rsp| {
-                        futures::future::ready(match rsp {
-                            zs::Response::Block(Some(block)) => Ok(Some(block)),
+                let mut state = self.state.clone();
+                async move {
+                    let mut blocks = Vec::new();
+                    for hash in hashes {
+                        let request = zs::Request::Block(hash.into());
+                        // we can't use ServiceExt::oneshot here, due to lifetime issues
+                        match state.ready_and().await?.call(request).await? {
+                            zs::Response::Block(Some(block)) => blocks.push(block),
                             // `zcashd` ignores missing blocks in GetData responses,
                             // rather than including them in a trailing `NotFound`
                             // message
-                            zs::Response::Block(None) => Ok(None),
+                            zs::Response::Block(None) => {}
                             _ => unreachable!("wrong response from state"),
-                        })
-                    })
-                    .try_collect::<Vec<_>>()
-                    .map_ok(zn::Response::Blocks)
-                    .boxed()
+                        }
+                    }
+                    Ok(zn::Response::Blocks(blocks))
+                }
+                .boxed()
             }
             zn::Request::TransactionsByHash(_transactions) => {
                 // `zcashd` returns a list of found transactions, followed by a