The reservoir volumetric approach represents a widely accepted, but flawed method of petroleum play resource calculation. In this paper, we propose a combination of techniques that can improve the applicability and quality of the resource estimation. These techniques include: 1) the use of the Multivariate Discovery Process model (MDP) to derive unbiased distribution parameters of reservoir volumetric variables and to reveal correlations among the variables; 2) the use of the Geo-anchored method to estimate simultaneously the number of oil and gas pools in the same play; and 3) the cross-validation of assessment results from different methods. These techniques are illustrated by using an example of crude oil and natural gas resource assessment of the Sverdrup Basin, Canadian Archipelago. The example shows that when direct volumetric measurements of the untested prospects are not available, the MDP model can help derive unbiased estimates of the distribution parameters by using information from the discovered oil and gas accumulations. It also shows that an estimation of the number of oil and gas accumulations and associated size ranges from a discovery process model can provide an alternative and efficient approach when inadequate geological data hinder the estimation. Cross-examination of assessment results derived using different methods allows one to focus on and analyze the causes for the major differences, thus providing a more reliable assessment outcome.