diff --git a/CHANGELOG.next.toml b/CHANGELOG.next.toml
index 23396d96ff..4e577e3fcf 100644
--- a/CHANGELOG.next.toml
+++ b/CHANGELOG.next.toml
@@ -11,8 +11,20 @@
 # meta = { "breaking" = false, "tada" = false, "bug" = false, "target" = "client | server | all"}
 # author = "rcoh"
 
+[[smithy-rs]]
+message = "Retry additional classes of H2 errors (H2 GoAway & H2 ResetStream)"
+references = ["aws-sdk-rust#738", "aws-sdk-rust#858"]
+meta = { "breaking" = false, "tada" = false, "bug" = false, "target" = "client" }
+author = "rcoh"
+
+[[aws-sdk-rust]]
+message = "Retry additional classes of H2 errors (H2 GoAway & H2 ResetStream)"
+references = ["aws-sdk-rust#738", "aws-sdk-rust#858"]
+meta = { "breaking" = false, "tada" = false, "bug" = false }
+author = "rcoh"
+
 [[aws-sdk-rust]]
 message = "Make some properties for IoT types optional. Previously, they defaulted to false, but that isn't how the service actual works."
 references = ["smithy-rs#3256"]
 meta = { "breaking" = true, "tada" = false, "bug" = true }
-author = "milesziemer"
+author = "milesziemer"
\ No newline at end of file
diff --git a/rust-runtime/aws-smithy-runtime/Cargo.toml b/rust-runtime/aws-smithy-runtime/Cargo.toml
index 6a3e1e40a1..d9ebaea92b 100644
--- a/rust-runtime/aws-smithy-runtime/Cargo.toml
+++ b/rust-runtime/aws-smithy-runtime/Cargo.toml
@@ -12,7 +12,7 @@ repository = "https://github.com/smithy-lang/smithy-rs"
 [features]
 client = ["aws-smithy-runtime-api/client"]
 http-auth = ["aws-smithy-runtime-api/http-auth"]
-connector-hyper-0-14-x = ["dep:hyper-0-14", "hyper-0-14?/client", "hyper-0-14?/http2", "hyper-0-14?/http1", "hyper-0-14?/tcp", "hyper-0-14?/stream"]
+connector-hyper-0-14-x = ["dep:hyper-0-14", "hyper-0-14?/client", "hyper-0-14?/http2", "hyper-0-14?/http1", "hyper-0-14?/tcp", "hyper-0-14?/stream", "dep:h2"]
 tls-rustls = ["dep:hyper-rustls", "dep:rustls", "connector-hyper-0-14-x"]
 rt-tokio = ["tokio/rt"]
 
@@ -28,6 +28,7 @@ aws-smithy-runtime-api = { path = "../aws-smithy-runtime-api" }
 aws-smithy-types = { path = "../aws-smithy-types", features = ["http-body-0-4-x"] }
 bytes = "1"
 fastrand = "2.0.0"
+h2 = { version = "0.3", default-features = false, optional = true }
 http = { version = "0.2.8" }
 http-body-0-4 = { package = "http-body", version = "0.4.4" }
 hyper-0-14 = { package = "hyper", version = "0.14.26", default-features = false, optional = true }
diff --git a/rust-runtime/aws-smithy-runtime/src/client/http/hyper_014.rs b/rust-runtime/aws-smithy-runtime/src/client/http/hyper_014.rs
index 0b5e6f056a..344c60714a 100644
--- a/rust-runtime/aws-smithy-runtime/src/client/http/hyper_014.rs
+++ b/rust-runtime/aws-smithy-runtime/src/client/http/hyper_014.rs
@@ -4,6 +4,7 @@
  */
 
 use crate::client::http::connection_poisoning::CaptureSmithyConnection;
+use crate::client::http::hyper_014::timeout_middleware::HttpTimeoutError;
 use aws_smithy_async::future::timeout::TimedOutError;
 use aws_smithy_async::rt::sleep::{default_async_sleep, AsyncSleep, SharedAsyncSleep};
 use aws_smithy_runtime_api::box_error::BoxError;
@@ -19,6 +20,7 @@ use aws_smithy_runtime_api::shared::IntoShared;
 use aws_smithy_types::body::SdkBody;
 use aws_smithy_types::error::display::DisplayErrorContext;
 use aws_smithy_types::retry::ErrorKind;
+use h2::Reason;
 use http::{Extensions, Uri};
 use hyper_0_14::client::connect::{capture_connection, CaptureConnection, Connection, HttpInfo};
 use hyper_0_14::service::Service;
@@ -397,21 +399,29 @@ fn downcast_error(err: BoxError) -> ConnectorError {
 
 /// Convert a [`hyper_0_14::Error`] into a [`ConnectorError`]
 fn to_connector_error(err: hyper_0_14::Error) -> ConnectorError {
-    if err.is_timeout() || find_source::<timeout_middleware::HttpTimeoutError>(&err).is_some() {
-        ConnectorError::timeout(err.into())
-    } else if err.is_user() {
-        ConnectorError::user(err.into())
-    } else if err.is_closed() || err.is_canceled() || find_source::<std::io::Error>(&err).is_some()
-    {
-        ConnectorError::io(err.into())
+    if err.is_timeout() || find_source::<HttpTimeoutError>(&err).is_some() {
+        return ConnectorError::timeout(err.into());
+    }
+    if err.is_user() {
+        return ConnectorError::user(err.into());
+    }
+    if err.is_closed() || err.is_canceled() || find_source::<std::io::Error>(&err).is_some() {
+        return ConnectorError::io(err.into());
     }
     // We sometimes receive this from S3: hyper::Error(IncompleteMessage)
-    else if err.is_incomplete_message() {
-        ConnectorError::other(err.into(), Some(ErrorKind::TransientError))
-    } else {
-        tracing::warn!(err = %DisplayErrorContext(&err), "unrecognized error from Hyper. If this error should be retried, please file an issue.");
-        ConnectorError::other(err.into(), None)
+    if err.is_incomplete_message() {
+        return ConnectorError::other(err.into(), Some(ErrorKind::TransientError));
     }
+    if let Some(h2_err) = find_source::<h2::Error>(&err) {
+        if h2_err.is_go_away()
+            || (h2_err.is_reset() && h2_err.reason() == Some(Reason::REFUSED_STREAM))
+        {
+            return ConnectorError::io(err.into());
+        }
+    }
+
+    tracing::warn!(err = %DisplayErrorContext(&err), "unrecognized error from Hyper. If this error should be retried, please file an issue.");
+    ConnectorError::other(err.into(), None)
 }
 
 fn find_source<'a, E: Error + 'static>(err: &'a (dyn Error + 'static)) -> Option<&'a E> {