A new NMR method is proposed for measuring anisotropic spin-Hamiltonian parameters, STEAMER (slow turning echo amplitude modulation and echo reduction). It involves slow turning of a powdered sample about an axis perpendicular to the external magnetic field. We have theoretically analyzed and experimentally demonstrated this technique for the specific case of an axially symmetric second-rank tensor interaction. The method relies upon a slow continuous rotation of the sample that changes the orientation of the principal-axis systems of interaction tensors with respect to the external magnetic field and renders the spin Hamiltonian time dependent. As a consequence a conventional Hahn spin-echo pulse sequence yields imperfect refocusing and altered echo amplitudes. Two principal advantages of STEAMER are that only a small portion of the entire powder pattern need be observed at a single frequency and that anisotropic interactions can be distinguished from distributions of isotropic interactions. The N-14 (I=1) selectively excited pi/2-pi spin-echo NMR signal in KNO3 provides a good test case for the effects of slow turning (rotation at 1 rpm) since it has a first-order quadrupole interaction from a N-14 nuclear quadrupole coupling constant (NQCC) of 0.75 MHz and a small asymmetry parameter (0.022), Theoretical simulations of the echo amplitude as a function of the pulse interval for an axially symmetric second-rank tensor agree well with the experimental results at a chosen frequency, These numerical simulations are compared to an analytical approximation derived in terms of the zeroth-order Bessel function. In addition, a simple graphical method for obtaining NQCC values from STEAMER data is developed. Other aspects and possible extensions of the STEAMER experiment are discussed.