This paper demonstrates the appearance of tangential discontinuities in deformed force-free fields by direct integration of the field equation ▿ xB= αB. To keep the mathematics tractable the initial field is chosen to be a layer of linear force-free fieldBx= +B0cosqz, By= —B0sinqz, Bz= 0, anchored at the distant cylindrical surface ϖ = (x2+y2)1/2=Rand deformed by application of a local pressure maximum of scalelcentered on the originx=y= 0. In the limit of largeR/lthe deformed field remains linear, with α =q[1 +O(l2/R2)]. The field equations can be integrated over ϖ =Rshowing a discontinuity extending along the lines of force crossing the pessure maximum. On the other hand, examination of thecontinuoussolutions to the field equations shows that specification of the normal component on the enclosing boundary ϖ =Rcompletely determines the connectivity throughout the region, in a form unlike the straight across connections of the initial field. The field can escape this restriction only by developing internal discontinuities.