We predict capillary-pressure (drainage) curves in tight-gas sandstones which have little matrix or microporosity using a quantitative grain-scale model. The model accounts for the geometric results of some depositional and diagenetic processes important for porosity and permeability reduction in tight-gas sandstones, such as deformation of ductile grains during burial and quartz cementation. The model represents the original sediment as a dense, disordered packing of spheres. We simulated the evolution of this model sediment into a low-porosity sandstone by applying different amounts of ductile grains and quartz precipitation. A substantial fraction of original pore throats in the sediment is closed by the simulated diagenetic alteration. Because the percolation threshold corresponds to closure of half of the pore throats, the pore space in this type of tight-gas sandstone is poorly connected and is often close to being completely disconnected. The drainage curve for different model rocks was computed using invasion percolation in a network taken directly from the grain-scale geometry and topology of the model. Some general trends follow classical expectations and were confirmed by experimental measurements: increasing the amount of cement shifts the drainage curve to larger pressures. This is related to reduction of the connectivity of pore space resulting from closure of throats. Existence of ductile grains in the ductile grain model also reduces the connectivity of pore space but it treats the throats distribution differently causing the drainage curves to be shifted to larger irreducible water saturation when cement is added to the model. The range of porosities in which these connectivity effects are important corresponds to the range of porosities common for tight gas sandstones. Consequently these rocks can exhibit small effective permeability to gas even at large gas saturations. This problem occurs at larger porosities in rocks with significant content of ductile grains because ductile deformation blocks a significant fraction of pore throats even before cementation begins. Predicted drainage curves agree with measurements on two samples with little microporosity, one dominated by rigid grains, the other containing a significant fraction of ductile grains. We conclude that connectivity of the matrix pore space is an important factor for an understanding of flow properties of tight-gas sandstones.