  We present new computations of tight shapes obtained using the constrained
gradient descent code RIDGERUNNER for 544 composite knots with 12 and fewer
crossings, expanding our dataset to 943 knots and links. We use the new data
set to analyze two outstanding conjectures about tight knots, namely that the
ropelengths of composite knots are at least 4\pi-4 less than the sums of the
prime factors and that the writhes of composite knots are the sums of the
writhes of the prime factors.
