The development of brain function in young infants is poorly understood. The core challenge is that infants have a limited behavioral repertoire through which brain function can be expressed. Neuroimaging with fMRI has great potential as a way of characterizing typical development, and detecting abnormal development early. But, a number of methodological challenges must first be tackled to improve the robustness and sensitivity of neonatal fMRI. A critical one of these, addressed here, is that the hemodynamic response function (HRF) in pre-term and term neonates differs from that in adults, which has a number of implications for fMRI. We created a realistic model of noise in fMRI data, using resting-state fMRI data from infants and adults, and then conducted simulations to assess the effect of HRF of the power of different stimulation protocols and analysis assumptions (HRF modeling). We found that neonatal fMRI is most powerful if block-durations are kept at the lower range of those typically used in adults (full on/off cycle duration 25-30s). Furthermore, we show that it is important to use the age-appropriate HRF during analysis, as mismatches can lead to reduced power or even inverted signal. Where the appropriate HRF is not known (for example due to potential developmental delay), a flexible basis set performs well, and allows accurate post-hoc estimation of the HRF. cusack_fmriFor each of five neonates, there is an fMRI timeseries (raw data) and a manually drawn grey matter mask. The adult data from this paper are already available from the fc1000 dataset.