It was recently demonstrated that one can perform fast nonlocal means (NLM) denoising of one-dimensional (1-D) signals using a method called lifting. The cost of lifting is independent of the patch length, which dramatically reduces the run-time for large patches. Unfortunately, it is difficult to directly extend lifting for NLM denoising of images. To bypass this, the authors proposed a separable approximation in which the image rows and columns are filtered using lifting. The overall algorithm is significantly faster than NLM, and the results are comparable in terms of PSNR. However, the separable processing often produces vertical and horizontal stripes in the image. This problem was previously addressed using a bilateral filter-based postsmoothing, which was effective in removing some of the stripes. We demonstrate that stripes can be mitigated in the first place simply by involving the neighboring rows (or columns) in the filtering. In other words, we use a two-dimensional (2-D) search (similar to NLM), while still using 1-D patches (as in the previous proposal). The innovation is in the observation that one can use lifting for performing 2-D searches. The proposed approach produces artifact-free images, whose quality and PSNR are comparable to NLM, while being significantly faster.