We discuss the implications of a PIXIE-like experiment, which would measure μ-type spectral distortions of the cosmic microwave background (CMB) at a level of σ μ ¼ ð1=nÞ × 10 −8 , with n ≥ 1 representing an improved sensitivity (e.g. n ¼ 10 corresponds to PRISM). Using Planck data and considering the six-parameter ΛCDM model, we compute the posterior for μ 8 ≡ μ × 10 8 and find μ 8 ¼ 1.57−0.52 (68% C.L.) when the running α s of the spectral index is included. We point out that a sensitivity of about 3 × PIXIE implies a guaranteed discovery: μ distortion is detected or α s ≥ 0 is excluded (both at 95% C.L. or higher). This threshold sensitivity sets a clear benchmark for CMB spectrometry. For a combined analysis of PIXIE and current Planck data, we discuss the improvement on measurements of the tilt n s and the running α s and the dependence on the choice of the pivot. A fiducial running of α s ¼ −0.01 (close to the Planck best fit) leads to a detection of negative running at 2σ for 5 × PIXIE. A fiducial running of α s ¼ −0.02, still compatible with Planck, requires 3 × PIXIE to rule out α s ¼ 0 (at 95% C.L.). We propose a convenient and compact visualization of the improving constraints on the tilt, running and tensor-to-scalar ratio.