Controlling streamer morphology is important for numerous applications. Up to now, the effect of the voltage rise rate was only studied across a wide range. Here we show that even slight variations in the voltage rise can have significant effects. We have studied positive streamer discharges in a 16 cm point-plane gap in high-purity nitrogen 6.0, created by 25 kV pulses with a duration of 130 ns. The voltage rise varies by a rise rate from 1.9 to 2.7 kV ns-1 and by the first peak voltage of 22 to 28 kV. A structural link is found between smaller discharges with a larger inception cloud caused by a faster rising voltage. This relation is explained by the greater stability of the inception cloud due to a faster voltage rise, causing a delay in the destabilization. Time-resolved measurements show that the inception cloud propagates slower than an earlier destabilized, more filamentary discharge. This explains that the discharge with a faster rising voltage pulse ends up being shorter. Furthermore, the effect of remaining background ionization in a pulse sequence has been studied, showing that channel thickness and branching rate are locally affected, depending on the covered volume of the previous discharge.