A fully microscopic model is used to calculate the carrier capture times in quantum-well lasers operating at wavelengths in the 1.3 mum regime. The capture times are shown to be crucially dependent on the carrier confinement and therefore on the well and barrier materials. For a common well width of 6 nm the capture times in InP/InGaAlAS and InP/InGaAsP structures are found to be in the 5 ps range, whereas about a factor of ten longer times are predicted in GaInNAs/GaAs. By lowering the barriers using GaInNAs instead of pure GaAs or widening the well capture times similar to those in the InP-based structures can be obtained in the GaInNAs-based structure.