Recent genetic studies as well as recorded history point to massive growth in human population sizes during the recent past. To model and understand this growth accurately we introduce FTEC, an easy-to-use coalescent simulation program capable of simulating haplotype samples drawn from a population that has undergone faster than exponential growth. Samples drawn from a population that has undergone faster than exponential growth show an excess of very rare variation and more rapid LD decay when compared with samples drawn from a population that has maintained a constant size over time.