The invention relates to truncated GLP-1 analogs, in particular a GLP-1 analog which is a modified GLP-1(7-35) (SEQ ID No 1) having: i) a total of 2, 3, 4, 5 6, 7, 8, or 9 amino acid substitutions as compared to GLP-1(7-35), including a) a Glu residue at a position equivalent to position 22 of GLP-1(7-35), and b) an Arg residue at a position equivalent to position 26 of GLP-1(7-35); as well as derivatives thereof, and therapeutic uses and compositions. These analogs and derivatives are highly potent, have a good binding affinity to the GLP-1 receptor, also to the extracellular domain of the GLP-1 receptor, which is of potential relevance achieving long-acting, stable GLP-1 compounds with a potential for once weekly administration.