  We study residually finite-dimensional (or RFD) operator algebras which may
not be self-adjoint. An operator algebra may be RFD while simultaneously
possessing completely isometric representations whose generating C*-algebra is
not RFD. This has provided many hurdles in characterizing residual
finite-dimensionality for operator algebras. To better understand the elusive
behaviour, we explore the C*-covers of an operator algebra. First, we equate
the collection of C*-covers with a complete lattice arising from the spectrum
of the maximal C*-cover. This allows us to identify a largest RFD C*-cover
whenever the underlying operator algebra is RFD. The largest RFD C*-cover is
shown to be similar to the maximal C*-cover in several different facets and
this provides supporting evidence to a previous query of whether an RFD
operator algebra always possesses an RFD maximal C*-cover. In closing, we
present a non self-adjoint version of Hadwin's characterization of separable
RFD C*-algebras.
