diff --git a/nexus/src/app/instance.rs b/nexus/src/app/instance.rs
index e916974332..a76980f27d 100644
--- a/nexus/src/app/instance.rs
+++ b/nexus/src/app/instance.rs
@@ -1610,11 +1610,19 @@ impl super::Nexus {
         if let Some(max_bytes) = params.max_bytes {
             request = request.max_bytes(max_bytes);
         }
-        if let Some(from_start) = params.from_start {
-            request = request.from_start(from_start);
-        }
-        if let Some(most_recent) = params.most_recent {
-            request = request.most_recent(most_recent);
+        match (params.from_start, params.most_recent) {
+            (Some(from_start), None) => {
+                request = request.from_start(from_start);
+            }
+            (None, Some(most_recent)) => {
+                request = request.most_recent(most_recent);
+            }
+            _ => {
+                return Err(Error::invalid_request(
+                    "Exactly one of 'from_start' \
+                    or 'most_recent' must be specified.",
+                ));
+            }
         }
         let data = request
             .send()
@@ -1714,29 +1722,36 @@ impl super::Nexus {
             match vmm.runtime.state {
                 DbVmmState::Running
                 | DbVmmState::Rebooting
-                | DbVmmState::Migrating => {
-                    Ok((vmm.clone(), SocketAddr::new(vmm.propolis_ip.ip(), vmm.propolis_port.into())))
-                }
+                | DbVmmState::Migrating => Ok((
+                    vmm.clone(),
+                    SocketAddr::new(
+                        vmm.propolis_ip.ip(),
+                        vmm.propolis_port.into(),
+                    ),
+                )),
 
                 DbVmmState::Starting
                 | DbVmmState::Stopping
                 | DbVmmState::Stopped
                 | DbVmmState::Failed
-                | DbVmmState::Creating => {
+                | DbVmmState::Creating
+                | DbVmmState::Destroyed
+                | DbVmmState::SagaUnwound => {
                     Err(Error::invalid_request(format!(
-                        "cannot connect to serial console of instance in state \"{}\"",
+                        "cannot administer instance in state \"{}\"",
                         state.effective_state(),
                     )))
                 }
 
-                DbVmmState::Destroyed | DbVmmState::SagaUnwound => Err(Error::invalid_request(
-                    "cannot connect to serial console of instance in state \"Stopped\"",
-                )),
+                DbVmmState::Destroyed | DbVmmState::SagaUnwound => {
+                    Err(Error::invalid_request(
+                        "cannot administer instance in state \"Stopped\"",
+                    ))
+                }
             }
         } else {
             Err(Error::invalid_request(format!(
-                "instance is {} and has no active serial console \
-                    server",
+                "instance is {} and cannot be administered",
                 state.effective_state(),
             )))
         }
diff --git a/nexus/tests/integration_tests/instances.rs b/nexus/tests/integration_tests/instances.rs
index 163869896f..a19d6ef27a 100644
--- a/nexus/tests/integration_tests/instances.rs
+++ b/nexus/tests/integration_tests/instances.rs
@@ -5430,6 +5430,8 @@ async fn test_instance_serial(cptestctx: &ControlPlaneTestContext) {
     // Make sure we get a 404 if we try to access the serial console before creation.
     let instance_serial_url =
         get_instance_url(format!("{}/serial-console", instance_name).as_str());
+    let instance_serial_stream_url =
+        get_instance_url(format!("{}/serial-console", instance_name).as_str());
     let error: HttpErrorResponseBody = NexusRequest::expect_failure(
         client,
         StatusCode::NOT_FOUND,
@@ -5517,6 +5519,47 @@ async fn test_instance_serial(cptestctx: &ControlPlaneTestContext) {
     }
     assert_eq!(&actual[..expected.len()], expected);
 
+    // Now try querying the serial output history endpoint with bad parameters.
+    // Check that the errors are indicative here.
+    let builder =
+        RequestBuilder::new(client, http::Method::GET, &instance_serial_url)
+            .expect_status(Some(http::StatusCode::BAD_REQUEST));
+
+    let error = NexusRequest::new(builder)
+        .authn_as(AuthnMode::PrivilegedUser)
+        .execute()
+        .await
+        .unwrap()
+        .parsed_body::<dropshot::HttpErrorResponseBody>()
+        .unwrap();
+
+    // We provided neither from_start nor most_recent...
+    assert_eq!(
+        error.message,
+        "Exactly one of 'from_start' or 'most_recent' must be specified.",
+    );
+
+    let builder = RequestBuilder::new(
+        client,
+        http::Method::GET,
+        &format!("{}&from_start=0&most_recent=0", instance_serial_url),
+    )
+    .expect_status(Some(http::StatusCode::BAD_REQUEST));
+
+    let error = NexusRequest::new(builder)
+        .authn_as(AuthnMode::PrivilegedUser)
+        .execute()
+        .await
+        .unwrap()
+        .parsed_body::<dropshot::HttpErrorResponseBody>()
+        .unwrap();
+
+    // We provided both from_start and most_recent...
+    assert_eq!(
+        error.message,
+        "Exactly one of 'from_start' or 'most_recent' must be specified.",
+    );
+
     // Request a halt and verify both the immediate state and the finished state.
     let instance = instance_next;
     let instance_next =
@@ -5527,6 +5570,53 @@ async fn test_instance_serial(cptestctx: &ControlPlaneTestContext) {
             > instance.runtime.time_run_state_updated
     );
 
+    // As the instance is now stopping, we can't connect to its serial console
+    // anymore. We also can't get its cached data; the (simulated) Propolis is
+    // going away.
+
+    let builder = RequestBuilder::new(
+        client,
+        http::Method::GET,
+        &instance_serial_stream_url,
+    )
+    .expect_status(Some(http::StatusCode::BAD_REQUEST));
+
+    let error = NexusRequest::new(builder)
+        .authn_as(AuthnMode::PrivilegedUser)
+        .execute()
+        .await
+        .unwrap()
+        .parsed_body::<dropshot::HttpErrorResponseBody>()
+        .unwrap();
+
+    assert_eq!(
+        error.message,
+        "cannot administer instance in state \"stopping\"",
+    );
+
+    // Have to pass some offset for the cached data request otherwise we'll
+    // error out of Nexus early on while validating parameters, before
+    // discovering the serial console is unreachable.
+    let builder = RequestBuilder::new(
+        client,
+        http::Method::GET,
+        &format!("{}&from_start=0", instance_serial_url),
+    )
+    .expect_status(Some(http::StatusCode::BAD_REQUEST));
+
+    let error = NexusRequest::new(builder)
+        .authn_as(AuthnMode::PrivilegedUser)
+        .execute()
+        .await
+        .unwrap()
+        .parsed_body::<dropshot::HttpErrorResponseBody>()
+        .unwrap();
+
+    assert_eq!(
+        error.message,
+        "cannot administer instance in state \"stopping\"",
+    );
+
     let instance = instance_next;
     instance_simulate(nexus, &instance_id).await;
     let instance_next =