Food security policies are usually costly and involve trade-offs. We investigated this issue by simulating three policy responses to rising world food prices, using the MAGNET model applied to the Middle East and North Africa. A policy of tackling agricultural food losses increases food consumption at lower costs and prices, with welfare gains forming an upper bound of the costs of tackling agricultural food losses. Whilst trade-offs occur as resources are drawn from elsewhere, they outperform a policy of reducing import tariffs by boosting agricultural and overall growth much more. This leads to a reduced rather than increased import dependency, and higher welfare gains. A policy of stimulating equal-sized economic growth via manufacturing and services does worse regarding food prices, consumption and import dependency, but generates slightly higher welfare gains. Given their potential to improve food security, measures to tackle food losses in agriculture should focus on cost-effective solutions.