We investigate ladder determinantal varieties defined by ideals of minors of Ε½ . possibly different sizes in the different regions the steps of one-sided ladders L. These varieties are an important generalization of the classical ladder determinan-Ε½ . tal varieties i.e., with equal-size minors since they are very closely related to Schubert varieties, this being the first main result of this paper. We show that they correspond to opposite cells in Schubert varieties in flag varieties of type A . In n consequence, one deduces the normality and the CohenαMacaulayness of these one-sided ladder determinantal varieties with ideals of mixed-size minors, as well as the fact that they have rational singularities. Next we show that, up to products by affine spaces, each of these varieties is a basic open set in a classical ladder Ε½ . determinantal variety i.e., with equal-size minors and that it contains as a basic open set another classical ladder determinantal variety. This result, along with a general localisation lemma used to show it, enables us to compute the divisor class group and singular locus of the coordinate rings of these varieties, as well as to determine when they are Gorenstein.