We propose that pressure anisotropy causes weakly collisional turbulent plasmas to self-organize so as to resist changes in magnetic-field strength . We term this effect “ magneto-immutability ” by analogy with incompressibility ( resistance to changes in pressure ) . The effect is important when the pressure anisotropy becomes comparable to the magnetic pressure , suggesting that in collisionless , weakly magnetized ( high- \beta ) plasmas its dynamical relevance is similar to that of incompressibility . Simulations of magnetized turbulence using the weakly collisional Braginskii model show that magneto-immutable turbulence is surprisingly similar , in most statistical measures , to critically balanced MHD turbulence . However , in order to minimize magnetic-field variation , the flow direction becomes more constrained than in MHD , and the turbulence is more strongly dominated by magnetic energy ( a nonzero “ residual energy ” ) . These effects represent key differences between pressure-anisotropic and fluid turbulence , and should be observable in the \beta \gtrsim 1 turbulent solar wind .