The optimal-interpolation data-assimilation technique is used to combine TIROS Operational Vertical Sounder total-ozone columns with the three-dimensional tracer transport model TM3. An ozone chemistry parametrization and dry deposition of ozone are added to the model to give it the ability to simulate realistic ozone profiles. Starting from a separable form of the forecast covariance matrix, the optimal interpolation equation can be rewritten into a horizontal and vertical analysis step. First, the two-dimensional ozone column measurements are analyzed using estimates for the horizontal error covariances. In the second step of the assimilation procedure the analysis increment for the column is distributed over the vertical model layers. This step depends only on a normalized vertical weight function which is equal to the vertical covariance. Three different estimates for this weight function are introduced, using either the ozone error covariance, or the ozone time variance, or the actual ozone mass to distribute column corrections in the vertical. A comparison with independent Total Ozone Mapping Spectrometer ozone observations shows a considerable improvement of the total ozone field due to assimilation. The model error growth is small, making it suitable for assimilating sparse measurements. Ozone profiles from the assimilation appear realistic and close to the ones observed by sondes. They are capable to describe dynamical features in the lower stratosphere. However, due to the absence of vertical information, the assimilation of ozone columns has only little impact on the shape of the vertical ozone profile, which is mainly determined by the transport.