We propose a computationally-efficient soft-output detector for multiple-input multiple-output channels based on augmented channel puncturing in order to reduce tree processing complexity. The proposed detector, dubbed augmented WL detector (AWLD), employs a punctured channel with a special structure derived by triangulizing the original channel in augmented form, followed by Gaussian elimination. We prove that these punctured channels are optimal in maximizing the lower-bound on the achievable information rate (AIR) based on a newly proposed mismatched detection model. We show that the AWLD decomposes into a minimum mean-square error (MMSE) prefilter and channel-gain compensation stages, followed by a regular unaugmented WL detector (WLD). It attains the same performance as the existing AIR partial marginalization (AIR-PM) detector, but with much simpler processing.