Digital magnetic and optical storage systems employing NRZI recording use (d, k) codes. The d-parameter specifies the minimum number of 0's occurring between 1's while the k-parameter specifies the maximum number of 0's between l's. The n-track (d,k) codes (denoted as (d,k;n) codes) are extensions of (d, k) codes for use in multiple-track systems. Instead of imposing each track to individually satisfy both constraints, (d,k;n) codes satisfy the d-constraint in each track individually while relaxing the k-constraint by allowing it to be satisfied jointly by the multiple tracks. Although (d,k;n) codes can provide significant capacity increases over (d, k) codes, they suffer from the fact that a single faulty track can cause loss of synchronization and hence, loss of the data on all tracks. Orcutt and Marcellin (see IEEE Trans. on Inform. Theory, Sept., 1993) introduced n-track (d,k) codes with a redundancy of r (denoted as (d,k;n,r) codes) which allow for r faulty tracks by mandating that all subsets of n-r tracks satisfy the joint k-constraint. We propose a new method to construct (d,k; n, r) codes. These codes have simple encoding and decoding schemes, gain a large part of the capacity increase possible when using (d,k; n,r) codes, and are considerably more robust to faulty tracks.