The inelastic earthquake response of existing, reinforced concrete buildings with an open ground story, designed according to the old Greek codes, is investigated before and after their seismic strengthening with steel braces restricted to the open ground stories. The seismic performance evaluation is based on Part 3 of Eurocode 8 for assessment and retrofitting of buildings. Three and five-story, symmetric and non-symmetric buildings are subjected to a set of seven pairs of synthetic accelerograms, compatible with the design spectrum, and conclusions are drawn regarding the effectiveness of the strengthening solutions. Seismic behavior of the selected models confirms results of previous work regarding the insufficient capacity of the open ground stories for design level earthquakes. It is also shown that strengthening only the weak ground story, a choice having the substantial advantage of low cost and continued usage of the building during its seismic retrofitting, can remove the inherent weakness without shifting the problem to the stories above and thus making such buildings at least as strong as those without a weak first story. This partial strengthening is possible for symmetric as well as eccentric buildings, in which torsion plays a further detrimental role.