A vital stage in the mathematical modelling of real-world systems is to calibrate a model’sparameters  to  observed  data.   Likelihood-free  parameter  inference  methods,  such  as  Ap-proximate Bayesian Computation,  build Monte Carlo samples of the uncertain parameterdistribution by comparing the data with large numbers of model simulations.  However, thecomputational expense of generating these simulations forms a significant bottleneck in thepractical  application  of  such  methods.   We  identify  how  simulations  of  cheap,  low-fidelitymodels have been used separately in two complementary ways to reduce the computationalexpense of building these samples, at the cost of introducing additional variance to the re-sulting parameter estimates.  We explore how these approaches can be unified so that costand  benefit  are  optimally  balanced,  and  we  characterise  the  optimal  choice  of  how  oftento  simulate  from  cheap,  low-fidelity  models  in  place  of  expensive,  high-fidelity  models  inMonte  Carlo  ABC  algorithms.   The  resulting  early  accept/reject  multifidelity  ABC  algo-rithm that we propose is shown to give improved performance over existing multifidelity andhigh-fidelity approaches.