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Summary form only given. For a single-mode laser it is generally believed that far above threshold the detected noise level is determined by the pump noise if the quantum efficiency of conversion from pump excitation quantum to detected photons is close to unity. This allows the generation of sub-shot noise light by operating a semiconductor laser far above threshold with a quiet pump. We have found, however, that weak nonorthogonality of the cavity eigenmodes can add significant Petermann excess noise. This seriously impedes intensity noise squeezing even for an effectively single mode laser, i.e. a laser in which the intensity noise of the lasing mode a equal to the intensity noise of the total light output. The crucial point is that nonorthogonality leads to effects in the intensity noise in first order of the non-lasing mode amplitudes, in contrast to the usually considered second-order multi-mode effects. We have extended the quantum Langevin approach for the intensity noise of a laser by incorporating the effect of the nonorthogonal cavity modes in a quantum mechanically consistent way. For the intensity noise far above threshold we find S=1+/spl eta/[2(K-1)+/spl epsiv/-1], where S is the intensity noise relative to shot noise, K is the Petermann K-factor, /spl eta/ the ratio of outcoupling loss and internal loss, /spl epsiv/ quantifies the noise of the pump (/spl epsiv/=0 quiet pump, /spl epsiv/=1 Poissonian pump). This formula clearly shows a very interesting result: for K/spl ges/1.5 the intensity noise, S, is always above shot noise and intensity squeezing is no longer possible. Experimental evidence confirms the theory.