The short answer here would be that semiconductor lasers typically operate with efficiencies above 50%, closer to 70%, so the easiest way to increase efficiency is to find a semiconductor laser that will substitute for your gas or solid-state laser.
The questioner appears more interested in fundamental limits, however. There is an intrinsic quantum limit on the efficiency of any laser. For Light Amplification by Stimulated Emission of Radiation (LASER) to occur, one must have optical _gain_ (for the amplification), and to have gain, one must have _population inversion_ in the gain medium. Population inversion refers to a situation in which a high-energy quantum state is more highly occupied than a lower energy state. To create such a state, it is necessary to involve other quantum states, typically two others, in a cascade process that is as follows:
a) Energy is pumped into the system, 0 -> 3 (states are numbered in order of increasing energy);
b) The system relaxes, 3 -> 2, releasing energy in the form of heat or non-laser light;
c) The system undergoes stimulated emission, releasing laser light and making the transition 2 -> 1;
d) The system again relaxes, 1 -> 0, and again releases energy in the form of heat or non-laser light.
Processes (b) and (d) are where the intrinsic inefficiencies lie. One must always pump more energy into the system (E3-E0) than one gets out in laser radiation (E2-E1). An additional important requirement is that processes (b) and (d) must occur much more rapidly than process (c), and this means in practice that most lasers that depend on atomic transitions have relatively low quantum efficiencies.
Semiconductor lasers have high quantum efficiencies because semiconductor technology enables us to engineer the quantum levels of the gain medium with much greater flexibility than atoms allow, to construct systems in which the simple act of passing current through the device forces the electrons into population inversion as they reach the junction between two dissimilar semiconducting materials.
Beyond these intrinsic inefficiencies, there are technical inefficiencies that also intervene. Absorption and imperfect mirrors in the cavity are obvious ones. There is also the efficiency with which the pump energy source can be coupled into the laser gain medium. There has been enormous recent improvements on this front, as people replace electrical discharge and flashlamp pump sources with laser diode pump sources. When used as a pump source, laser diodes can be focused effectively on the gain medium for maximum energy extraction, improving efficiencies over flashlamp pumps by factors of two or more.