In the EDGE EDITING TO CONNECTED f-DEGREE GRAPH problem we are given a graph G, an integer k, and a function f assigning integers to vertices of G. The task is to decide whether there is a connected graph F on the same vertex set as G, such that for every vertex v, its degree in F is f(v), and the number of edges in E(G)\bigtriangleup E(F), the symmetric difference of E(G) and E(F), is at most k. We show that EDGE EDITING TO CONNECTED f-DEGREE GRAPH is fixed-parameter tractable (FPT) by providing an algorithm solving the problem on an n-vertex graph in time 2\scrO (k)n\scrO (1). We complement this result by showing that the weighted version of the problem with costs 1 and 0 is W[1]-hard when parameterized by k and the maximum value of f even when the input graph is a tree. Our FPT algorithm is based on a nontrivial combination of color-coding and fast computations of representative families over the direct sum matroid of \ell -elongation of the co-graphic matroid associated with G and a uniform matroid over the set of nonedges of G. We believe that this combination could be useful in designing parameterized algorithms for other edge editing and connectivity problems. © 2019 Society for Industrial and Applied Mathematics