TPS62135: Better efficiency with 100% Duty Cycle Mode

Dear Sir, 

Please advise if there has one part has better efficiency than TPS62135 at the condition of 5.6Vin, 3.8Vout, 3~4A Iout.

Feature needed : 
100% Duty Cycle mode
Power Good Output
Vin is 4V~6V
Iout 3 ~ 4A

Suppose TPS62088 or TPS62095 may be better, but it's input only up to 5.5V.  Target operate Vin need to be 6V or 6.5V.

Thanks,
Hugo