In addition to e-APIS, you must telephone in advance with your ETA, number of pax, citizenships, aircraft type and registration. Here is the
guide listing the airports of entry, hours, phone numbers.
If your aircraft is not N registered you may need a TSA exemption unless coming from Canada, Bermuda, Bahamas, Cayman Islands, Mexico, or the British VI AND your aircraft is registered to one of these countries/colonies.
Without the TSA exemption you will not be allowed to enter US airspace unless you departed one of the entry countries. This is a stupid rule and is a carry-over from 9/11, but our government never rescinds rules because of the jobs-worths. e-APIS was to replace this requirement.
Lastly, you must have a Customs decal on your aircraft (valid for one calendar year). It must be applied for on-line and it is sent by post.
Link to obtaining a decal.
The TSA Border Overflight Exemptions can be obtained on-line
here or through Universal, Jeppesen, etc.