The bi-Kappa distribution models anisotropic space-plasma populations with suprathermal power-law tails. Kinetic simulations represent such a population by computational particles, and a loader draws their velocities from the requested bi-Kappa distribution, which we call the target distribution. When $\kappa$ is close to $1/2$, floating-point underflow can remove the largest draws, and a velocity bound changes the loaded distribution. Published Kappa loaders are usually verified by comparing histograms of the speed or of one velocity component with the analytic distribution. Such comparisons do not examine the direction of the velocity or whether the direction is independent of the speed. We build an anisotropic loader on an established Gamma-ratio construction and examine each of these problems. Near $\kappa =1/2$, evaluating the Gamma ratio on a logarithmic scale avoids the loss of draws to underflow in single and double precision down to $\kappa =0.5001$. When draws outside a bound on each velocity component are discarded and redrawn, a small rejected fraction can accompany a large change in the tail. At $\kappa =2$ and ${\theta }_{\parallel }=2{\theta }_{\perp }$, a bound at 20 times each component’s thermal speed rejects a fraction $3.6\times {10}^{-4}$ of the draws and lowers the 99.9th-percentile speed by 11%. We test the loaded velocities through their direction and their normalized radius, the length of the velocity after each component is divided by $\sqrt{\kappa }$ times its thermal speed. The tests used nine values of $\kappa$ from 0.51 to 10, including $1/2<\kappa \le 3/2$, where the second moments do not exist, with ${\theta }_{\parallel }=2{\theta }_{\perp }$ in double precision. At every $\kappa$, ${\chi }^2$ tests find the normalized radius out to its 99.999th percentile, the direction, and their joint distribution consistent with the target distribution. The loader and a program that applies these tests to velocities from other loaders are released as open-source software.