diff --git a/proxy/src/auth/backend/classic.rs b/proxy/src/auth/backend/classic.rs
index d8ee1e8b64d7..46bd215f3b25 100644
--- a/proxy/src/auth/backend/classic.rs
+++ b/proxy/src/auth/backend/classic.rs
@@ -5,7 +5,7 @@ use crate::{
     auth::{self, AuthFlow, ClientCredentials},
     compute,
     console::{self, AuthInfo, CachedNodeInfo, ConsoleReqExtra},
-    proxy::handle_try_wake,
+    proxy::{handle_try_wake, retry_after},
     sasl, scram,
     stream::PqStream,
 };
@@ -62,10 +62,13 @@ pub(super) async fn authenticate(
             }
             Ok(ControlFlow::Continue(e)) => {
                 warn!(error = ?e, num_retries, retriable = true, "couldn't wake compute node");
-                num_retries += 1;
             }
             Ok(ControlFlow::Break(n)) => break n,
         }
+
+        let wait_duration = retry_after(num_retries);
+        num_retries += 1;
+        tokio::time::sleep(wait_duration).await;
     };
     if let Some(keys) = scram_keys {
         use tokio_postgres::config::AuthKeys;
diff --git a/proxy/src/proxy.rs b/proxy/src/proxy.rs
index e6fcf901d974..0267d767eec5 100644
--- a/proxy/src/proxy.rs
+++ b/proxy/src/proxy.rs
@@ -545,7 +545,7 @@ impl ShouldRetry for compute::ConnectionError {
     }
 }
 
-fn retry_after(num_retries: u32) -> time::Duration {
+pub fn retry_after(num_retries: u32) -> time::Duration {
     // 1.5 seems to be an ok growth factor heuristic
     BASE_RETRY_WAIT_DURATION.mul_f64(1.5_f64.powi(num_retries as i32))
 }