The performance of the restricted-open-shell form of the double-hybrid density functional theory (DHDFT) B2-PLYP procedure has been compared with that of its unrestricted counterpart using the G3/05 test set. Additionally, the influence of basis set on the parametrization and performance of ROB2-PLYP, and the further improvement of ROB2-PLYP through augmentation with a long-range dispersion function, have been investigated. We find that, after optimization of the two empirical DHDFT parameters, the ROB2-PLYP method (HF exchange = 59% and MP2 correlation = 28%) performs slightly better than the corresponding UB2-PLYP method (HF exchange = 62% and MP2 correlation = 35%), with mean absolute deviations (MADs) from the experimental energies in the G3/05 test set of 9.1 and 9.9 U mol(-1), respectively, when the cc-pVQZ basis set is employed. Separate optimizations of the parameters for the RO and U procedures are crucial for a fair comparison. For example, for the G2/97 test set, ROB2-PLYP(53,27) and ROB2-PLYP(62,35) show MADs of 12.2 and.13.5 U mol(-1), respectively, compared with the 6.6 U mol(-1) for (the optimized) ROB2-PLYP(59,28). The performance of ROB2-PLYP deteriorates significantly as the basis-set size is decreased, reflecting the enhanced basis-set dependence of the MP2 contribution compared with standard DFT. We find that this deficiency can be partly overcome through reparametrization. However, when the basis set drops below triple-zeta, the improvements made on reoptimizing the ROB2-PLYP parameters are not sufficient to warrant their general use. We find that the dispersion- and BSSE-corrected ROB2-PLYP(59,28)-D HCP procedure performs significantly better than ROB2-PLYP(59,28) for the S22 test set of interaction energies in which dispersion interactions are particularly important, with the MAD failing from 6.1 to 1.6 U mol(-1). However, when the same D correction is applied to the G3/05 test set, the performance of ROB2-PLYP(59,28)-D deteriorates slightly compared with ROB2-PLYP(59,28), with the MAD increasing from 9.1 to 9.5 U mol(-1).