In general, two possible ways to get H4 EAD quicker than a normal process: 1. H4 and H4 EAD applications with H1B application + Premium Processing (In most cases, H4 and H4 EAD applications will be approved with H1B within 15 days.) 2. Requests to Expedite Application (USCIS will determine whether the case meets their criteria. It takes a couple of days to several weeks.) http://www.uscis.gov/policymanual/HTML/PolicyManual-Volume1-PartA-Chapter12.html