Industrial requirements for accuracy in metal sheet components are typically ±0.2 mm where current incremental sheet forming processes are capable of an accuracy of only ±3 mm. Several approaches based on process design modifications or control strategies are being developed to overcome this problem, but none has as yet been entirely successful. This paper proposes and examines a new approach in which the area to be formed within the blank is “partially cut-out” using a water jet or laser cutter. The aim of this partial cut-out is to localise deformation to the area over which the tool travels and thus reduce the difference between a part made by a “contour tool path” and the target product geometry. Several design options are considered, and the approach is evaluated with one simple and one complex part. The results indicate that partially cut-out blanks lead to slightly more accurate forming than conventional blanks when unsupported, but that the accuracy improvement is less than that which is achieved by use of a stiff cut-out supporting plate. The results include an experimental investigation of residual stresses and springback in incremental sheet forming.