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We investigate theoretically the slowdown of optical pulses due to quantum-coherence effects in InGaAs-based quantum dots and quantum dot molecules. Simple models for the electronic structure of quantum dots and, in particular, quantum-dot molecules are described and calibrated using numerical simulations. It is shown how these models can be used to design optimized quantum-dot molecules for quantum coherence applications. The wave functions and energies obtained from the optimizations are used as input for a microscopic calculation of the quantum-dot material dynamics including carrier scattering and polarization dephasing. The achievable group velocity slowdown in quantum-coherence V schemes consisting of quantum-dot molecule states is shown to be substantially higher than what is achievable from similar transitions in typical InGaAs-based single quantum dots.