If the words “offshore entity” inspire dreams of Caribbean islands and easy compliance because, well, there are hardly any tax or governance rules to comply with—you may want to wake up to reality.

That reality is that there are a dwindling number of benefits to incorporating in offshore tax havens such as Bermuda or the British Virgin Islands, thanks to more muscular and more uniform enforcement from the Internal Revenue Service, the European Union, and other regulators trying to extend their cross-border reach.