This paper focuses on tractable instances of interval data minmax regret graph problems. More precisely, we provide polynomial and pseudopolynomial algorithms for sets of particular instances of the interval data minmax regret versions of the shortest path, minimum spanning tree and weighted (bipartite) perfect matching problems. These sets are defined using a parameter that measures the distance from trivial instances. Tractable cases occur when the parameter is bounded by a constant. Two kinds of parameters are investigated, measuring either the distance from special weight structures or the distance from special graph structures.