Osteoporotic fractures are a key health problem in older men. Although there are drugs approved to treat osteoporosis in men \[bisphosphonates, denosumab, and teriparatide (TPTD) or PTH(1-34)\], there is a lack of knowledge on how to use them effectively. TPTD is a potent bone anabolic drug, meaning that it builds bone mass. However, doctors do not know if it should only be used as single drug or whether it can be more effectively combined to achieve the most benefit? This trial will test a novel combination therapy for osteoporosis in men based on exciting laboratory findings in mice. TPTD works to raise bone mass and improve bone strength by stimulating PTH receptors (PTH-Rs) on the membranes of bone-forming cells or osteoblasts (OBs). Calcimimetics are drugs that activate calcium receptors (CaSRs) in OBs. CaSRs in OBs participate in new bone formation. Daily injections of TPTD, given along with a calcimimetic drug (called NPS-R568), over 6 weeks markedly improved bone mineral density (BMD) and structure in mice. This study will test whether the combined activation of PTH-Rs and CaSRs (by the combination treatment of TPTD+calcimimetic cinacalcet) in men will produce greater bone forming responses than PTH-R activation alone (TPTD+placebo). The study has two aims and will be done in 48 men with low bone mass: (1) to determine the effects of 11 months treatment with TPTD+cinacalcet vs TPTD+placebo on BMD and bone metabolism by assessing lumbar spine BMD (primary endpoint), femoral neck BMD, and levels of the bone formation marker serum N-terminal pro-peptide of type 1 collagen; (2) to determine the biochemical responses by blood tests in men who receive the combination of TPTD+cinacalcet compared to men who get TPTD+placebo treatment. This is done by quantifying acute and chronic changes in serum calcium and PTH levels right after these drugs are given and how much calcium is excreted in the urine over time, with both treatment regimens. This study will help to understand whether an effective combination therapy in mice will prove to be effective in men.