We demonstrate the possibility of Bose-Einstein condensation (BEC) of an ideal Bose gas confined by one-and two-dimensional power-law traps. One-dimensional systems display BEC in traps that are more confining than parabolic: U (x)∼ x η, η< 2. Two-dimensional systems display BEC for any finite value of η. A possible experimental configuration for a two-dimensional trap is described.