In 1H MAS spectra, the residual homogeneous broadening under MAS is due to a combination of higher-order shifts and splittings. We have recently shown how the two-dimensional anti-z-COSY experiment can be used for the removal of the splittings. However, this requires spectra with high resolution in the indirect dimension (t1), leading to experiment times of hours. Here, we show how anti-z-COSY can be adapted to be combined with the two-dimensional one pulse (TOP) transformation which leads to significantly reduced experimental time while retaining the line narrowing effect. The experiment is demonstrated on a powdered sample of L-histidine monohydrochloride monohydrate, where the new TAZ-COSY sequence at 100 kHz MAS, yields between a factor 1.6 and 2.3 increase in resolution compared with the equivalent one-pulse experiment, in just 20 min. The same methodology is also adapted for the acquisition of liquid state 1H homodecoupled data, and an example is given for testosterone.