The concept of adaptive two-stage designs is applied to the problem of testing the equality of several normal means against an ordered (monotone) alternative. The likelihood-ratio-test proposed by Bartholomew is known to have favourable power properties when testing against a monotonic trend. Tests based on contrasts provide a flexible way to incorporate available information regarding the pattern of the unknown true means through appropriate specification of the scores. The basic idea of the presented concept is the combination of Bartholomews test (first stage) with an "adaptive score test" (second stage) which utilizes the information resulting from isotonic regression estimation at the first stage. Several results of an extensive Monte Carlo simulation study will be reported concerning the power behaviour of these combination tests. This approach will be of special interest if, e.g., sample size reassessment is incorporated.