Issues controlling efficient parallel implementations of a popular direct search inversion algorithm are analyzed and discussed. A naive parallelization of a particular method, the Neighbourhood parameter search algorithm, leads to inefficient use of parallel architecture through lack of scalability and intolerance to hardware faults. These factors are quantified, and their origins are explained. A reformulation of the algorithm leads to dramatically improved performance when the cost of the forward problem is low and the number of unknowns is high. Numerical examples are used to illustrate the main results. Factors in the original Neighbourhood Algorithm which lead to poor parallel performance are likely to be present in other ensemble-based inversion or global optimization algorithms. Hence the algorithmic solutions proposed may have widespread application.