The IceCube detector took data in its 22-string configuration in 2007-2008. This data has been analyzed to search for extraterrestrial point sources of neutrinos using several methods. Two main methods are discussed and compared here: the binned and the unbinned maximum likelihood method. The best sky-averaged sensitivity (90% C.L.) is E2 Φνμ = 1.3 × 10- 11 TeVcm- 2 s- 1 to a generic E-2 flux of νμ over the energy range from 3 TeV to 3 PeV. No neutrino point sources are found from the individual directions of a pre-selected catalogue nor in a search extended to the northern sky. Limits are improved by a factor of two compared to the total statistics collected with the AMANDA-II detector and represent the best results to date. © 2009 Elsevier B.V. All rights reserved.