We discuss the reduction of the critical dimension of open strings in the fermionic construction. Requiring the preservation of supersymmetry and finiteness, we find one consistent type-I theory with a minimal number of sectors in each of the space-time dimensions 9, 7, 6, 5, 3, and 2. Each of these is "mixed" in that there are sectors containing both Neveu-Schwarz and Ramond fields. No consistent open-string solution of this type is found for D = 4 .
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