We show that, for a TM (or p-state) Gaussian beam incident onto an absorbing medium at and around Brewster's dip, the reflected beam always remains Gaussian and undergoes a Goos-Hänchen-like (GH) shift, an angular shift, a focal shift, and a beam-waist modification, provided that the beam is sufficiently collimated that the third-order change of the (logarithmic) reflection coefficient can be ignored in the angular range of beam divergence. For weak absorption, not only are a large negative GH shift and an odd-functioned-like focal shift with greater magnitude found but also the angular shift, though small by itself, is shown to give an even larger lateral net shift at a distance beyond the Rayleigh range.