Given a bipartite graph G=(V
c
,V
t
,E) and a nonnegative integer k, the NP‐complete Minimum‐Flip Consensus Tree problem asks whether G can be transformed, using up to k edge insertions and deletions, into a graph that does not contain an induced P
5 with its first vertex in V
t
(a so‐called M‐graph or ∑‐graph). This problem plays an important role in computational phylogenetics, V
c
standing for the characters and V
t
standing for taxa. Chen et al. (2006). showed that Minimum‐Flip Consensus Tree is NP‐complete and presented a parameterized algorithm with running time O(6
k
⋅|V
t
|⋅|V
c
|). Subsequently, Böcker et al. (2012) presented a refined search tree algorithm with running time O(4.42
k
(|V
t
|+|V
c
|)+|V
t
|⋅|V
c
|). We continue the study of Minimum‐Flip Consensus Tree parameterized by k. Our main contribution are polynomial‐time executable data reduction rules yielding a problem kernel with O(k
3) vertices. In addition, we present an improved search tree algorithm with running time O(3.68
k
⋅|V
c
|2|V
t
|).
