In sp2013 rest, you can get json returned. But also depending on the header type, you can specify a no metadata option to get less data as shown here.
However in all the examples I've seen, this is for a non-search rest call. Combined with this:
Does anyone know what combination of url paramaters with their values to use to minimize the data being returned from a search rest query? I am only interested in the result set and no other data.