High storage density and high data rate are two of the most desired properties of modern hard disk drives. Heat-assisted magnetic recording (HAMR) is believed to achieve both. Recording media, consisting of exchange-coupled grains with a high and a low T C part, were shown to have low dc noise-but increased ac noise-compared to hard magnetic single-phase grains like FePt. We extensively investigate the influence of an Fe-Rh interlayer on the magnetic noise in exchange-coupled grains. We find an optimal grain design that reduces the jitter in the down-track direction by up to 30% and in the off-track direction by up to 50%, depending on the head velocity, compared to the same structures without FeRh. Furthermore, the mechanisms causing this jitter reduction are demonstrated. Additionally, we show that, for short heat pulses and low write temperatures, the switching-time distribution of the analyzed grain structure is reduced by a factor of 4 compared to the same structure without an Fe-Rh layer. This feature could be interesting for HAMR use with a pulsed laser spot and could encourage discussion of this HAMR technique.