Improved diode laser beam combining techniques are in strong demand for applications in material processing. Coherent beam combining (CBC) is the only combining approach that has the potential to maintain or even improve all laser properties, and thus has high potential for future systems. As part of our ongoing studies into CBC of diode lasers, we present recent progress in the coherent superposition of high-power single-pass tapered laser amplifiers. The amplifiers are seeded by a DFB laser at λ = 976 nm, where the seed is injected into a laterally single-mode ridge-waveguide input section. The phase pistons on each beam are actively controlled by varying the current in the ridge section of each amplifier, using a sequential hill-climbing algorithm, resulting in a combined beam with power fluctuations of below 1%. The currents into the tapered sections of the amplifiers are separately controlled, and remain constant. In contrast to our previous studies, we favour a limited number of individual high-power amplifiers, in order to preserve a high extracted power per emitter in a simple, low-loss coupling arrangement. Specifically, a multi-arm interferometer architecture with only three devices is used, constructed using 6 mm-long tapered amplifiers, mounted junction up on C-mounts, to allow separate contact to single mode and amplifier sections. A maximum coherently combined power of 12.9 W is demonstrated in a nearly diffraction-limited beam, corresponding to a 65% combining efficiency, with power mainly limited by the intrinsic beam quality of the amplifiers. Further increased combined power is currently sought.