We investigate the consequences of flat dark matter-dominated cosmogonies with hybrid isocurvature and adiabatic initial perturbations, and with a Harrison-Zel'dovich primordial spectrum normalized to the COBE-Differential Microwave Radiometer (DMR) 2 yr measurements. We show that, while the COBE-DMR data alone shows no preference for a specific admixture of these modes, acceptable combinations are strongly constrained by other observational data. Nevertneless, the character of the initial conditions cannot be uniquely resolved on that basis, and, in some cases, a suitable mixture of both modes still may be used in an attempt to avoid some of the observed problems of purely adiabatic models. Specifically, we consider critical density, cold dark matter (CDM) and mixed dark matter (MDM) models. In the latter case, we show that an isocurvature contribution of order ～50%-60% (when expressed in terms of the contribution to the present-day quadrupole) allows for a reasonably good fit to existing observational data. Low total density CDM-dominated models with any significant admixture of isocurvature mode are excluded, while CDM models with critical total density and hybrid initial conditions do not provide a significantly better fit to the data than purely adiabatic scalar models, and then only if the possibility of high-amplitude pairwise velocities on a 1 h~(-1) Mpc scale is considered.
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