Heteronuclear correlation (HETCOR) spectroscopy is one of the key tools in the arsenal of the solid-state NMR spectroscopist to probe spatial proximity between two different nuclei and enhance spectral resolution. Dipolar heteronuclear multiple-quantum coherence (D-HMQC) is a powerful technique that can be potentially utilized to obtain 1H detected 2D HETCOR solid-state NMR spectra of any NMR active nucleus. A long-standing problem in 1H detected D-HMQC solid-state NMR experiments is the presence of t1-noise which reduces sensitivity and impedes spectral interpretation. In this contribution, we describe novel pulse sequences, termed t1-noise eliminated (TONE) D-HMQC, that suppress t1-noise and can provide higher sensitivity and resolution than conventional D-HMQC. Monte-Carlo and numerical simulations confirm that t1-noise in conventional D-HMQC primarily occurs because random MAS frequency fluctuations cause variations in the NMR signal amplitude from scan to scan, leading to imperfect cancellation of uncorrelated signals by phase cycling. The TONE D-HMQC sequence uses 1H p-pulses to refocus the evolution of 1H CSA across each recoupling block, improving the stability of the pulse sequence to random MAS frequency fluctuations. The 1H refocusing pulses also restore the orthogonality of in-phase and anti-phase magnetization for all crystallite orientations, enabling the use of 90° flip-back or LG spin-lock trim pulses to reduce the intensity of uncorrelated signals. We demonstrate the application of these methods to acquire detected 2D 1H-35Cl and 1H-13C HETCOR spectra of histidine•HCl•H2O with reduced t1-noise. To show generality, we also apply these methods to obtain 2D 1H-17O spectra of 20%-17O fmoc-alanine and for the first time at natural abundance, 2D 1H-25Mg HETCOR spectra of magnesium hydroxide. The TONE D-HMQC sequences are also used to probe 1H-25Mg and 1H-27Al proximities in Mg-Al layered double hydroxides and confirm the even mixing of Mg and Al in these materials.