A method for deploying a floating platform at an offshore wellsite uses pull-down lines to provide stability to the platform while ballasting. The platform is equipped with a number of tension devices and towed to a staging site while at a first draft, At the staging site, the operator connects lines from the sea floor to the tension devices on the platform. The operator gradually adds ballast to the platform and simultaneously applies tension to the lines with the tension devices. When at a desired second draft, the operator detaches the lines and tows the platform to a well site. The platform is moored with a catenary mooring system at the well site.