An analysis of the alternatives of compensation in relation tointernational investment disputes is relevant, because a pecuniary award is not always the appropriate remedy to solve disputes arising between investors and States. This is the case because States may be increasingly interested in opting for a different type ofcompensation. Furthermore, it is still not clear whether arbitraltribunals have recognised alternative types of awarding damages inrespect of international investments disputes. This analysiscomprises two principal components, the first, is toidentify whether or not the tribunals may render an award that notonly demands the payment of a sum of money but also considers someother means of compensation. The second, centres on how compliancewith these non-pecuniary awards may be demanded.Our approach to these two principal components will always revolvearound the idea of respecting the sovereignty of the State, bearingin mind that the execution of an arbitral award, which obliges the State to refrain from or to perform an act in its territory, reliesprecisely on the sovereignty of the State to execute it.