H-1B visas are tied to a specific employer. The fact that you can move between different employers who will individually agree to sponsor a H-1B position doesn'

H-1B visas are tied to a specific employer. The fact that you can move between different employers who will individually agree to sponsor a H-1B position doesn't change that fact. This is fine when you're talking about moving between large companies with the apparatus to do that, but it does mean that H-1B holders have fewer opportunities with smaller employers or those who simply aren't willing to go through the paperwork.