We propose a new approach to explain the unusually low pressure coefficients of the luminescence peaks observed in single-quantum-well InGaN-based light emitting diodes manufactured by Nichia Chemical Industries. In view of the most recent first principles band structure calculations for InN under hydrostatic pressure, we find that it is possible to reproduce the measured low (12–16meV/GPa) pressure coefficients of the luminescence by assuming the formation of zincblende InN inclusions in the InGaN quantum well layers. These cubic inclusions, surrounded by the usual wurtzite material, should act like quantum dots giving rise to enhanced electron localization. Obtained this way, the pressure shift of the luminescence peaks in blue and green InGaN-based emitters should be close to 14meV/GPa, in good agreement with our experimental results. This explanation of the observed low pressure coefficients in these devices is consistent with recent independent evidence for InN inclusions in InGaN epilayers.