diff --git a/milli/src/vector/error.rs b/milli/src/vector/error.rs
index 3673c85e3..fbe4ee878 100644
--- a/milli/src/vector/error.rs
+++ b/milli/src/vector/error.rs
@@ -59,8 +59,8 @@ pub enum EmbedErrorKind {
     OpenAiAuth(OpenAiError),
     #[error("sent too many requests to OpenAI: {0}")]
     OpenAiTooManyRequests(OpenAiError),
-    #[error("received internal error from OpenAI: {0}")]
-    OpenAiInternalServerError(OpenAiError),
+    #[error("received internal error from OpenAI: {0:?}")]
+    OpenAiInternalServerError(Option<OpenAiError>),
     #[error("sent too many tokens in a request to OpenAI: {0}")]
     OpenAiTooManyTokens(OpenAiError),
     #[error("received unhandled HTTP status code {0} from OpenAI")]
@@ -106,7 +106,7 @@ impl EmbedError {
         Self { kind: EmbedErrorKind::OpenAiTooManyRequests(inner), fault: FaultSource::Runtime }
     }
 
-    pub(crate) fn openai_internal_server_error(inner: OpenAiError) -> EmbedError {
+    pub(crate) fn openai_internal_server_error(inner: Option<OpenAiError>) -> EmbedError {
         Self { kind: EmbedErrorKind::OpenAiInternalServerError(inner), fault: FaultSource::Runtime }
     }
 
diff --git a/milli/src/vector/openai.rs b/milli/src/vector/openai.rs
index cbddddfb7..cfc4b6e83 100644
--- a/milli/src/vector/openai.rs
+++ b/milli/src/vector/openai.rs
@@ -220,24 +220,12 @@ impl Embedder {
                         error_response.error,
                     )));
                 }
-                StatusCode::INTERNAL_SERVER_ERROR => {
-                    let error_response: OpenAiErrorResponse = response
-                        .json()
-                        .await
-                        .map_err(EmbedError::openai_unexpected)
-                        .map_err(Retry::retry_later)?;
+                StatusCode::INTERNAL_SERVER_ERROR
+                | StatusCode::BAD_GATEWAY
+                | StatusCode::SERVICE_UNAVAILABLE => {
+                    let error_response: Result<OpenAiErrorResponse, _> = response.json().await;
                     return Err(Retry::retry_later(EmbedError::openai_internal_server_error(
-                        error_response.error,
-                    )));
-                }
-                StatusCode::SERVICE_UNAVAILABLE => {
-                    let error_response: OpenAiErrorResponse = response
-                        .json()
-                        .await
-                        .map_err(EmbedError::openai_unexpected)
-                        .map_err(Retry::retry_later)?;
-                    return Err(Retry::retry_later(EmbedError::openai_internal_server_error(
-                        error_response.error,
+                        error_response.ok().map(|error_response| error_response.error),
                     )));
                 }
                 StatusCode::BAD_REQUEST => {
@@ -248,14 +236,14 @@ impl Embedder {
                         .map_err(EmbedError::openai_unexpected)
                         .map_err(Retry::retry_later)?;
 
-                    tracing::warn!("OpenAI: input was too long, retrying on tokenized version. For best performance, limit the size of your prompt.");
+                    tracing::warn!("OpenAI: received `BAD_REQUEST`. Input was maybe too long, retrying on tokenized version. For best performance, limit the size of your prompt.");
 
                     return Err(Retry::retry_tokenized(EmbedError::openai_too_many_tokens(
                         error_response.error,
                     )));
                 }
                 code => {
-                    return Err(Retry::give_up(EmbedError::openai_unhandled_status_code(
+                    return Err(Retry::retry_later(EmbedError::openai_unhandled_status_code(
                         code.as_u16(),
                     )));
                 }