Nonphysical sampling Monte Carlo techniques that enable average structural properties of short in vacuo polypeptide chains to be calculated accurately are discussed. Updating algorithms developed for Monte Carlo studies of flexible polymer chains are modified and adapted for polypeptide chain systems to improve conformational sampling. Utilizing these methods, the effect of bond angle and bond length constraints in Monte Carlo simulations are examined and it is demonstrated that angle constraints bias structural averages without greatly reducing the computational work.