Theoretical calculations on the influence of both an external electric field and hydrostatic stress on the binding energy and impurity polarizability of shallow-donor impurities in an isolated GaAs-(Ga, Al)As quantum well are presented. A variational procedure within the effective-mass approximation is considered. The pressure-related Γ-X crossover is taken into account. As a general feature, we observe that the binding energy increases as the length of the well decreases. For the low-pressure regime we observe a linearly binding energy behaviour. For the high-pressure regime the simultaneous effects of the barrier height and the applied electric field bend the binding energy curves towards smaller values. For low hydrostatic pressures the impurity polarization remains constant in all cases with an increasing value as the field increases. This constant behaviour shows that the small variations in well width, effective mass, and dielectric constant with pressure do not appreciably affect polarizability. For high hydrostatic pressure, we see a non-linear increase in polarizability, mainly due to the decrease of barrier height as a result of the external pressure, which allows further deformation of the impurity.