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.