Multi-loop matter-wave interferometers are essential in quantum sensing to extract physical quantities and their derivatives in time or space. They are realized by stacking several mirror stages, but the finite efficiency of the matter-wave mirrors creates spurious paths which scramble the signal of interest. Here we demonstrate a method of adjustable momentum transfer that prevents the recombination of the spurious paths in a double-loop cold-atom interferometer aimed at measuring rotation rates. We experimentally study the recombination condition of the spurious matter waves, which is quantitatively supported by a model accounting for the coherence properties of the atomic source. We finally demonstrate the effectiveness of the method in building a cold-atom gyroscope with zero residual acceleration sensitivity. Our study will impact the design of multi-loop atom interferometers that measure a unique inertial quantity. Matter-wave interference is a central concept of quantum mechanics with a myriad of applications making use of electrons [1], neutrons [2], or atoms and molecules [3]. Examples of applications range from bacteria characterization [4] and biomolecular analysis [5], to fundamental physics tests [6] and accurate inertial sensing [7]. In most cases, a required high degree of control over the interference conditions and the precision of a measurement rely on the interference of two waves, with a sinusoidal fringe pattern providing direct access to the phase shift. The presence of auxiliary interferometic loops due to the imperfection of the mirrors, may, on the contrary, result in a multiple-wave interference that scrambles the signal of interest even in the absence of the noise sources. Light-pulse atom interferometers employ a train of so-called atom optics elements-dedicated laser pulses that split, deflect and recombine the atomic waves making them follow spatially distinct trajectories enclosing in the simplest case a single loop, in a geometry similar to that of an optical Mach-Zehnder interferometer. Accessing spatial derivatives of physical quantities (e.g. gradients of magnetic or gravitational fields) or a selective measurement of one among several contributions often requires interferometers consisting of several loops [8, 9], realized by multiple deflection of the matter-waves with additional mirrors-a technique analogous to the multi-pulse magnetic resonance spectroscopy [10]. The finite transmission of the atomic mirrors leads to the appearance of spurious leaked matter waves, which, in presence of additional mirrors, become redirected and eventually form closed interferometric loops, degrading the two-wave nature of the interferometer [11]. Understanding and controlling the recombination of these spurious paths is intimately linked to the coherence of the matter-wave source, and requires a tailored design of the interferometric sequence and atomic mirrors. In this Letter, we report on a method which prevents the recombination of the spurious paths in multi-loop cold-atom interferometers, both in position and in momentum space. Our method uses atomic mirrors transferring an adjustable momentum to the atom. The high degree of control provided by this method, compared to other techniques in matter-wave interferometry, enables the detailed, though general, study of the process of the recombination of wave-packets. Finally, we show that the method of adjustable momentum transfer (AMT) allows for building a pure-rate gyroscope, as theoretically proposed in Ref. [12]. Our results can be generalized to atom-interferometric sensors of arbitrary multi-loop ar-chitectures. We implement the AMT method in a double-loop atom interferometer aimed at measuring rotation rates and described in Refs. [13, 14]. In short, we laser-cool Cesium atoms in a single internal state |F = 4 to the temperature of 1.8 µK, and launch them vertically using moving molasses in an atomic fountain. The atom optics employ stimulated Raman transitions at 852 nm that couple the |F = 3 and |F = 4 internal states with two counter-propagating laser fields of wave-vectors k 3 and k 4 , imparting a momentum k eff = (k 3 − k 4) to the diffracted part of the wave-packet [15]. The inter-ferometric sequence comprising four Raman laser pulses of π/2, π, π, π/2 Rabi angles, forms a symmetric double-loop path diagram of the split wave-packets, which will be discussed in detail later. The resulting accumulated phase difference is read out from the probability of transition between the two internal states using fluorescence detection and internal-state labeling of the output ports of the interferometer [16]. Two pairs of Raman beams access the interrogation region from two collimators as shown in Fig. 1(a). Each pair is retro-reflected by a mirror. The mirrors are parallel to each other to better than 0.2 µrad [17] and tilted by an angle θ 0 = 3.8 • with respect to the horizontal direc-tionx, in order to lift the degeneracy between the ± k eff transitions owing to the Doppler effect. The top collima-tor can be further inclined by a small adjustable angle arXiv:2006.08371v1 [physics.atom-ph]