This paper presents preliminary results from a new comprehensive calculation of effective recombination rate coefficients for electrons and ions in finite density plasma. The principal point at issue is the dielectronic component of the effective recombination and it is this which is emphasised here. The modern viewpoint of dielectronic recombination commences with the paper of Burgess (1964). Burgess (1965) also provided a 'General Formula' for the total dielectronic recombination coefficient, valid in the zero density limit, of great simplicity. It, and variants, have been widely used to the present time. A number of points arise. Firstly, the dielectronic coefficient is sensitive to the density of the plasma so that a density correction to the General Formula is required (Burgess & Summers, 1969). Secondly there is the question of the intrinsic accuracy of the atomic cross-section assumptions made in deriving the General Formula. It has been pOinted out that the General Formula appears to overestimate when the target ion transition involved is of type Dn1 (Mertz et ai, 1976). Thirdly there are omitted effects such as alternative Auger channels (Jacobs et al 1977). Finally, the role of metastable states in the recombining and recombined ion is generally ignored.