Threshold determination within the framework of the block up‐and‐down, two‐interval, forced‐choice (BUDTIF) method has been investigated using a computerized Monte Carlo technique. Two aspects of the results are presented in preliminary fashion. (1) In a block up‐and‐down threshold‐estimating method, modifications that yield minimal variance within individual runs may not automatically be assumed to yield minimal variance between successive threshold estimates. (2) The optimal number of trials per block was the smallest that yields a valid solution depending on the target performance level; use of a memory of more than one block for level change decisions is not indicated.