jats:pThe 46- and 69-residue BLN model proteins both exhibit frustrated folding to β-barrel structures. We study the effect of varying the strength of nonnative interactions on the corresponding energy landscapes by introducing a parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:miλ</mml:mi></mml:math>, which scales the potential between the BLN (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:mrowmml:miλ</mml:mi>mml:mo=</mml:mo>mml:mn1</mml:mn></mml:mrow></mml:math>) and Gō-like (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:miλ</mml:mi>mml:mo=</mml:mo>mml:mn0</mml:mn></mml:math>) limits. We study the effect of varying <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:miλ</mml:mi></mml:math> on the efficiency of global optimisation using basin-hopping and genetic algorithms. We also construct disconnectivity graphs for these proteins at selected values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:miλ</mml:mi></mml:math>. Both methods indicate that the potential energy surface is frustrated for the original BLN potential but rapidly becomes less frustrated as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:miλ</mml:mi></mml:math> decreases. For values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:miλ</mml:mi>mml:mo≤</mml:mo>mml:mn0.9</mml:mn></mml:math>, the energy landscape is funnelled. The fastest mean first encounter time for the global minimum does not correspond to the Gō model: instead, we observe a minimum when the favourable nonnative interactions are still present to a small degree.</jats:p>