Providing indirect data addressing in an input/output processing system where the indirect data address list is non-contiguous

A computer program product for processing input/output (I/O) data is provided for performing a method that includes receiving a transport control word (TCW) including an indirect data address including a starting location of a transport mode indirect data address list (TIDAL) of storage addresses, the TIDAL including a plurality of entries configured as transport mode indirect data address words (TIDAWs). The method includes accessing an entry of the TIDAL, which includes: 1) based on the entry of the TIDAL indicating that the address is a data address, gathering data from a data storage location corresponding to the data address, and accessing a next entry of the TIDAL, and 2) based on the entry of the TIDAL indicating that the address is an address of a next entry of the TIDAL, obtaining the next entry of the TIDAL from another storage location that is located non-contiguously to the entry storage location.