diff --git a/dist/unstable/httpapi/HttpApiSchema.js b/dist/unstable/httpapi/HttpApiSchema.js
index c51851b..2100420 100644
--- a/dist/unstable/httpapi/HttpApiSchema.js
+++ b/dist/unstable/httpapi/HttpApiSchema.js
@@ -151,7 +151,7 @@ export const StreamSse = options => {
   const events = options.events ?? (options.data === undefined ? undefined : Schema.Struct({
     id: Schema.UndefinedOr(Schema.String),
     event: Schema.String,
-    data: Schema.fromJsonString(options.data)
+    data: sseDataJsonSchema(options.data)
   }));
   if (events === undefined) {
     throw new Error("StreamSse requires either an events schema or a data schema");
@@ -166,6 +166,14 @@ export const StreamSse = options => {
     error: options.error ?? Schema.Never
   });
 };
+const sseDataJsonSchema = data => {
+  const identifier = SchemaAST.resolveIdentifier(data.ast);
+  return identifier === undefined ? Schema.fromJsonString(data) : Schema.fromJsonString(data).annotate({
+    // The SSE transport field is a JSON string. Give that wrapper its own
+    // OpenAPI identifier so it does not claim the decoded data schema's name.
+    identifier: `${identifier}Stream`
+  });
+};
 /**
  * Creates a streaming `Uint8Array` success response schema.
  *
diff --git a/src/unstable/httpapi/HttpApiSchema.ts b/src/unstable/httpapi/HttpApiSchema.ts
index aae6cd5..f05e3ed 100644
--- a/src/unstable/httpapi/HttpApiSchema.ts
+++ b/src/unstable/httpapi/HttpApiSchema.ts
@@ -407,7 +407,7 @@ export const StreamSse: {
   const events = options.events ?? (options.data === undefined ? undefined : Schema.Struct({
     id: Schema.UndefinedOr(Schema.String),
     event: Schema.String,
-    data: Schema.fromJsonString(options.data)
+    data: sseDataJsonSchema(options.data)
   }))
   if (events === undefined) {
     throw new Error("StreamSse requires either an events schema or a data schema")
@@ -423,6 +423,15 @@ export const StreamSse: {
   })
 }
 
+const sseDataJsonSchema = (data: Schema.Constraint) => {
+  const identifier = SchemaAST.resolveIdentifier(data.ast)
+  return identifier === undefined ? Schema.fromJsonString(data) : Schema.fromJsonString(data).annotate({
+    // The SSE transport field is a JSON string. Give that wrapper its own
+    // OpenAPI identifier so it does not claim the decoded data schema's name.
+    identifier: `${identifier}Stream`
+  })
+}
+
 /**
  * Creates a streaming `Uint8Array` success response schema.
  *
