A general weakness of instruction pipelines is ‘bubbles’ or ‘holes’ in the pipeline due to conditional branch instructions. Most of the solutions (Lee and Smith 1984) to the branch problem attempt to predict whether or not a branch will be taken. If the prediction is correct, then the correct sequence of instructions can be initiated without delay. The performance of an instruction pipeline is analyzed to give a measure of the efficiency or utilisation of the pipeline segments in terms of the probability of correct branch prediction (referred to as the prediction accuracy). The analysis is based on the space-time relationship. The performance of an instruction pipeline with both equal and unequal segment times is analysed incorporating the effect of two types of conditional branch instructions in the instruction sets of computers. The results of the analysis enable one to study the sensitivity of the performance of an instruction pipeline to the number of conditional branch instructions and the probability of correct branch prediction as well as to estimate the utility of the different branch prediction strategies that have been proposed recently (Lee and Smith 1984). Although it is extremely difficult to obtain the value of 1 for prediction accuracy, this study reveals that a value of 0.8 can give reasonably good values of utilization.