This study is a multi-center, double-blind, placebo-controlled, multiple dose escalating, safety, tolerance, pharmacokinetics, and efficacy study of fipamezole administered in Parkinson's disease patients who are concomitantly being treated with a combination product of levodopa with a dopamine decarboxylase inhibitor (DDI) and possible other antiparkinson medication. Approximately 30 sites in the US and India will participate in this study. The patients will be randomized into one of four treatment arms to receive either fixed or ascending doses of Fipamezole (from 30 to 90 mg tid) or placebo. For efficacy assessments, levodopa-induced dyskinesia is assessed using a standardised rating scale. Time spent in 'Off' state or in 'On' state without dyskinesia, 'On' with non-troublesome dyskinesia or 'On' with troublesome dyskinesia, is assessed using patient diaries. Impact of dyskinesia on daily activities is quantified using a PDYS-26 questionnaire. To explore potential positive or negative impact of Fipamezole on cognitive functions, the study includes two cognitive tests. Finally, the study includes investigator assessments of CGI-I scales for dyskinesia, Parkinson's disease, and clinical condition in general.