The recent accelerated expansion of the Brazilian economy, from 2004 to 2007, was driven by exports and gross fixed capital formation. Although this pace of growth is more robust than it was in the 1990s, we can still witness the presence of macroeconomic constraints to its continuation in the long term, such as the exchange rate overvaluation, particularly since 2005, and in general the modus operandi of monetary policy. Such constraints may jeopardise the sustainability of the current pace of growth. We argue that Brazil still lies in a trap made up of high interest and low exchange rates. The elimination of the exchange rate misalignment would bring about a large increase in the rate of interest, which in turn would impact negatively upon investment and hence upon long-term growth. We indicate a set of policy measures to eliminate such a trap, in particular, the adoption of an implicit exchange rate target, capital controls and the substitution of the present regime of inflation targeting with a 'double mandate regime' where monetary authorities must pursue two objectives, i.e. output stabilisation and inflation control. Recent events seem to go in this direction.