Recent progress in the development of superconducting nanowire single-photon detectors (SNSPDs) made of amorphous material has delivered excellent performances, and has had a great impact on a range of research fields. Despite showing the highest system detection efficiency (SDE) ever reported with SNSPDs, amorphous materials typically lead to lower critical currents, which impacts on their jitter performance. Combining a very low jitter and a high SDE remains a challenge. Here, we report on highly efficient superconducting nanowire single-photon detectors based on amorphous MoSi, combining system jitters as low as 26 ps and a SDE of 80% at 1550 nm. We also report detailed observations on the jitter behaviour, which hints at intrinsic limitations and leads to practical implications for SNSPD performance.