Disease spreading through human travel networks has been a topic of great interest in recent years, as witnessed during outbreaks of influenza A (H1N1) or SARS pandemics. One way to stop spreading over the airline network are travel restrictions for major airports or network hubs based on the total number of passengers of an airport. Here, we test alternative strategies using edge removal, cancelling targeted flight connections rather than restricting traffic for network hubs, for controlling spreading over the airline network. We employ a SEIR metapopulation model that takes into account the population of cities, simulates infection within cities and across the network of the top 500 airports, and tests different flight cancellation methods for limiting the course of infection. The time required to spread an infection globally, as simulated by a stochastic global spreading model was used to rank the candidate control strategies. The model includes both local spreading dynamics at the level of populations and long-range connectivity obtained from real global airline travel data. Simulated spreading in this network showed that spreading infected 37% less individuals after cancelling a quarter of flight connections between cities, as selected by betweenness centrality. The alternative strategy of closing down whole airports causing the same number of cancelled connections only reduced infections by 18%. In conclusion, selecting highly ranked single connections between cities for cancellation was more effective, resulting in fewer individuals infected with influenza, compared to shutting down whole airports. It is also a more efficient strategy, affecting fewer passengers while producing the same reduction in infections. The network of connections between the top 500 airports is available under the resources link on our website http://www.biological-networks.org.