Branching bisimilarity is a behavioural equivalence relation on labelled transition systems (LTSs) that takes internal actions into account. It has the traditional advantage that algorithms for branching bisimilarity are more efficient than ones for other weak behavioural equivalences, especially weak bisimilarity. With m the number of transitions and n the number of states, the classic O(mn) algorithm was recently replaced by an O(m(log |Act| + log n)) algorithm [Groote/Jansen/Keiren/Wijs, ACM ToCL 2017], which is unfortunately rather complex. This paper combines its ideas with the ideas from Valmari [PETRI NETS 2009], resulting in a simpler O(m log n) algorithm. Benchmarks show that in practice this algorithm is also faster and often far more memory efficient than its predecessors, making it the best option for branching bisimulation minimisation and preprocessing for calculating other weak equivalences on LTSs.