We study quasi-wetting transitions in confined systems in which capillary condensation is suppressed. In particular, we are concerned with adsorbates between opposing walls (one wall favours wetting, the other drying). We employ an Ising model and calculate the global phase diagram for a slab of width L and boundaries with opposite surface fields, in Landau theory. We find novel first-order, critical, and tricritical quasi-wetting transitions, which converge smoothly, for L --> infinity, to the familiar wetting transitions. We question the recently proposed novel mechanism for critical-point shifts in films.