SyncApi for DeletedEntry pertaining to a specific content_type only

According to the documentation: we are able to leverage the SyncApi to retrieve the latest deltas since the last import.
For Entry, we are able to specify the content_type flag and it will sync for us accordingly.
In this same analogy, I assumed that the same would apply for DeletedEntry, where we can specify a specific content_type according to which the SyncApi will give us the latest deleted entries for that specific content type only. When I submit my query like this:
curl -v$CONTENTFUL_SPACES_ID/sync\?initial\=true\&type\=DeletedEntry\&content_type\=house -H "Authorization: Bearer $CONTENTFUL_BEARER_TOKEN"

then it gives me an empty response.

The following works:
curl -v$CONTENTFUL_SPACES_ID/sync\?initial\=true\&type\=DeletedEntry -H "Authorization: Bearer $CONTENTFUL_BEARER_TOKEN"

but then it will give me all deleted entries, regardless their content type.

Is this an API limitation or is there anything I am overlooking?