In a weakly collisional, low-electron-beta plasma, large-scale Alfvén turbulence transforms into inertial kinetic-Alfvén turbulence at scales smaller than the ion microscale (gyroscale or inertial scale). We propose that at such kinetic scales, the nonlinear dynamics tends to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale a in the plane perpendicular to the guide field. This aspect ratio is defined by the balance of the eddy turnover rate and the tearing rate, and varies from (de/a) 1/2 to de/a depending on the assumed profile of the current sheets. The energy spectrum of the resulting turbulence varies from k −8/3 to k −3 , and the corresponding spectral anisotropy with respect to the strong background magnetic field from kz k 2/3 ⊥ to kz k ⊥ .PACS numbers: 52.35. Ra, 52.35.Vd, 52.30.Cv Introduction. Large-scale low-frequency fluctuations in astrophysical systems such as the interstellar medium, the solar wind, and others, are associated with nearly incompressible magnetohydrodynamic (Alfvén) turbulence [e.g., 1-3]. The nonlinear Alfvén wave packets that compose such turbulence are three-dimensionally anisotropic: elongated along the strong background magnetic field and resembling current sheets in the perpendicular plane [1,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. At scales smaller than the plasma microscales, such as the ion gyroscale or ion inertial scale, the shear-Alfvén modes transform into kinetic Alfvén modes. The character of turbulence then changes qualitatively. Numerical and analytical studies suggest that the energy spectrum becomes relatively steep in the sub-proton range, with the spectral index between −7/3 and −8/3, and fluctuations become compressible, with density and magnetic field fluctuations comparable to each other [e.g., 22-27]. Available solar wind measurements broadly agree with these predictions, with the measured energy spectral slope scattered around a slightly steeper value −2.8 [28][29][30][31][32].