Channel puncturing transforms a multiple-input multiple-output (MIMO) channel into a sparse lower-triangular form using the so-called WL decomposition scheme in order to reduce tree-based detection complexity. We propose computationally efficient soft-output detectors based on two forms of channel puncturing: augmented and two-sided. The augmented WL detector (AWLD) employs a punctured channel derived by triangularizing the true channel in augmented form, followed by leftsided Gaussian elimination. The two-sided WL detector (dubbed WLZ) employs right-sided reduction and left-sided elimination to puncture the channel. We prove that augmented channel puncturing is optimal in maximizing the lower-bound on the achievable information rate (AIR) based on a new mismatched detection model. We show that the AWLD decomposes into an MMSE prefilter and channel gain compensation stages, followed by a regular WL detector (WLD) that computes least-squares softdecision estimates. Similarly, WLZ decomposes into a pre-processing reduction step followed by WLD. AWLD attains the same performance as the existing AIR-based partial marginalization (PM) detector, but with less computational complexity. We empirically show that WLZ attains the best complexityperformance tradeoff among tree-based detectors.