If a classical Nambu-Goto string in $D$ dimensions is required to have Poincaré invariance in $d$ dimensions, $d<D$, then new boundary conditions involving free parameters whose numbers depend on $D-d$ are allowed. We quantize these new string theories and show that the restricted Poincaré invariance still requires $D=26\mathrm{}$. However, it allows choices of free parameters such that tachyons can be eliminated from the mass spectrum if $d<~10$. The new boundary conditions imply generalized Fubini-Veneziano commutation rules.

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