A semiempirical theoretical model is developed for estimating the rates of collision-induced V-T vibrational relaxation from an initially excited vibrational state in a polyatomic molecule to a relatively dense field of destination vibrational states. The rationale has been to provide a means of estimating absolute relaxation rate coefficients, with a reasonable level of precision, for relaxation induced by a wide range of collision partners (atomic, diatomic, and polyatomic) and for a relatively wide range of temperatures. The model is based on calculating an efficiency P for the vibrational relaxation process by making use of relevant known molecular and intermolecular parameters. The inelastic rate coefficient for vibrational relaxation then emerges from a product of this efficiency and the classical Lennard-Jones elastic encounter rate. A feature of the model is that it uses no adjustable parameters. Comparisons are made between the predictions from the model and a number of experimental measurements of specific dependencies of vibrational relaxation rate coefficients (e.g. on collision partner properties, on the initial vibrational state, and on temperature) to characterize and illustrate the ingredients that deliver the estimate for P. A correlation between the predictions of the model and data from over 100 experimental systems and for a temperature range from 2-300 K invites the conclusion that the model is useful for estimating the absolute magnitude of state-to-field vibrational relaxation rate coefficients in the intermediate regime of final state densities to within an overall accuracy of 30% and with an average error of -10%.