Electromagnetic induction systems have proven to be very effective in detecting subsurface metallic and magnetic objects. Such systems often employ separate transmit and receive coils, and thus it is desirable for the transmit and receive coils in these systems to have minimal mutual coupling. It is also desirable for the product of the fields generated by the transmit and receive coils to be as large as possible to maximize the detection depth. We demonstrate that a pair of spiral coils can be optimized to achieve these desired properties. A mathematical representation is chosen for the coils, which allows the coil pair to be optimized using an iterative convex method, which, due to its convexity, is very fast. We then present results showing a pair of nonuniformly wound spiral coils created with this optimization.