Parameter estimation (PE) for compact binary coalescence (CBC) events observed by gravitational wave (GW) laser interferometers is a core task in GW astrophysics. I will present a method to compute the posterior distribution efficiently without relying on stochastic samplers. This will involve first selecting sets of intrinsic and extrinsic parameters that efficiently cover the relevant phase space. I will then show how to compute the likelihood for all combinations of these parameters using dot products. The low computational cost allows full PE in minutes on a single CPU, with the potential for further acceleration using multiple CPUs or GPUs. This method can enable sensitive searches using the full evidence integral for GW sources with non-trivial dynamics like orbital precession and eccentricity with minimal computing resources.