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The so-called Affine Projection (AP) algorithm is of large interest in many adaptive filters applications due to its considerable speed-up in convergence compared to its simpler version, the LMS algorithm. While the original AP algorithm is well understood, gradient type variants of less complexity with relaxed step-size conditions called pseudo affine projection offer still unresolved problems. This contribution shows i) local robustness properties of such algorithms, ii) global properties of these, concluding ℓ2-stability conditions that are independent of the input signal statistics, as well as iii) steady-state values of moderate to high accuracy by relatively simple terms when applied to long filters. Of particular interest is the existence of lower step-size bounds for one of the variants, a bound that has not been observed before.