Basically Fission Bomb efficiency depends significantly on the neutron flux intensity before it blows itself apart hence the elements to be considered are
- the mechanism used to achieve supercritical mass
- the “neutron boosting” strategy
Regarding the critical mass generation mechanism as far as I can remember Little Boy’s used a gun type one and it was very inefficient (under 2%) 
A great improvement of one order of magnitude  has been first tested on Fat Man and fine tuned later using Explosive Lens  to transform a divergent wavefront created by conventional explosive into a convergent one. This technique is used to create an implosion to achieve a critical mass much larger than any gun type mechanism can produce.
Regarding the neutron boosting strategy it basically exploits the high temperature reached at the first stages of the fission chain reaction to trigger nuclear fusion in a small quantity of deuterium and tritium so to produce extra neutron and increase the effective flux interacting with the fuel.
Boosting should allow for another order of magnitude improvement with respect to implosion-only devices.