Will point sources spoil 21-cm tomography?

21-cm tomography is emerging as a promising probe of the cosmological dark ages and the epoch of reionization, as well as a tool for observational cosmology in general. However, serious sources of foreground contamination must be subtracted for experimental efforts to be viable. In this paper, we focus on the removal of unresolved extragalactic point sources with smooth spectra, and evaluate how the residual foreground contamination after cleaning depends on instrumental and algorithmic parameters. A crucial but often ignored complication is that the synthesized beam of an interferometer array shrinks towards higher frequency, causing complicated frequency structure in each sky pixel as 'frizz' far from the beam centre contracts across unresolved radio sources. We find that current-generation experiments should none the less be able to clean out this point source contamination adequately, and quantify the instrumental and algorithmic design specifications required to meet this foreground challenge.