The dawn of the age of gravitational wave astronomy heralds exciting results and new challenges. Chief among these is an accurate theory of binary mergers. When two massive stars in a binary survive their two supernovae, and produce a pair of Neutron Stars, they can merge, producing a Gravitational Wave transient event. Critically, then, providing a consistent estimate of the merger rates of compact binaries, as well as accurately predicting the period-eccentricity distributions of such binaries, is of utmost importance. We investigate the mechanism for natal supernova kicks, and in particular attempt to refine the Bray kick, which is governed by the equation vkick = αQ+ β, where Q is the ejecta-remnant mass ratio. We find that the kick has a characteristic slope α and offset β of either α = 110±5 km/s, β = 0 km/s or α = 40 ±5 km/s, β = 100 ±5 km/s. These parameters are sufficient to replicate the LIGO O3 data results. We find that α = 110 ±5 km/s, β = 0 km/s has a merger rate of log (R0 / yr−1 Gpc−3) = 2.5140 ±0.0002, and α = 40 ±5 km/s, β = 100 ±5 km/s has a merger rate of log (R0 / yr−1 Gpc−3) = 2.526 ±0.009. Moreover we find that the β = 0 model has the lowest frequency of highly eccentric extant NSNS systems out of all models considered, however this frequency exceeds our conservative requirements. We present a consistent and intuitive method for computing period-eccentricity distributions, and compute these for the models considered. We use this to illustrate the importance of predicting certain pulsars such as J1930-1852 (Swiggum et al., 2015). Consequently, we conclude that if the Bray kick is correct, it must be incomplete, and conjecture a new model for the Bray kick for future research to consider.