The ditopic ligands 3,5-dimethyl-pyrazolate-4-carboxylate, ^–Me₂pzCO₂^–, and 4-(3,5-dimethyl-1H-pyrazol-4-yl)benzoate, ^–Me₂pzC₆H₄CO₂^–, combine a pyrazolate and carboxylate functionality in axial orientation and lead to porous cobalt or zinc azolate–carboxylate frameworks that have the same cubic pcu-a topology and {M₄(μ₄-O)} nodes (M = Co, Zn) as MOF-5 and other IRMOFs. The microporous networks [M₄(μ₄-O)(Me₂pzCO₂)₃] (M = Co, Zn) with the short linker exhibit a solvent-induced gate effect, evidenced by gas desorption hysteresis due to small pore apertures of 2.8 Å diameter together with small amounts of high-boiling solvent remaining in the activated samples. For [Co₄(μ₄-O)(Me₂pzCO₂)₃], the low-pressure H₂ storage capacity (1.7 wt%, 1 bar , 77 K) is higher than for MOF-5, and the CO₂ uptake of 20.8 wt% puts it among the top MOFs for low-pressure CO₂ sorption even though the BET surface is less than 1000 m² g⁻¹. The analysis of the magnetic properties of [Co₄(μ₄-O)(Me₂pzCO₂)₃] takes into account the distribution of tetrahedra resulting from the disorder of the pyrazolate–carboxylate linker. An antiferromagnetic coupling observed for [Co₄(μ₄-O)(Me₂pzCO₂)₃] arises from the interactions of the cobalt(II) ions through the combined μ₄-O + syn–syn carboxylate and μ₄-O + pyrazolate bridges.