Experimental studies into the beam parameter product (BPP) of 940-980 nm GaAs-based high-power diode lasers are presented. Such lasers exhibit broadening far field and narrowing near field with increasing bias, with BPP increasing tenfold over the diffraction limit. First, spectrally-resolved beam profile measurements of lasers with monolithically-integrated gratings are presented, showing that a reproducible series of spatially-extended optical modes makes up the optical field. Then, changes to the device construction are presented, enabling effects limiting BPP to be inferred and addressed. Process- and package-induced effects can be minimized by design, while the effects of carrier, gain and temperature profiles dominate. Self-heating within the laser stripe raises the refractive index, forming a thermal lens, and the variation in curvature of this lens with bias and device construction directly affects BPP. Temperature non-uniformity along the resonator is also shown to strongly degrade BPP. Moreover, current spreading and the resulting lateral carrier accumulation (LCA) amplify high-order, high-BPP modes, thus degrading BPP for any given thermal lens. This LCA-induced degradation is shown to be suppressed by regrown lateral current-blocking structures. Finally, a flatter thermal lens and lower BPP can be achieved using thermal engineering, via changes to the epitaxial design or device layout.