In modern hospitals, monitoring patients’ vital signs and other biomedical signals is standard practice. With the advent of data-driven healthcare, Internet of medical things, wearable technologies, and machine learning, we expect this to accelerate and to be used in new and promising ways, including early warning systems and precision diagnostics. Hence, we see an ever-increasing need for retrieving, storing, and managing the large amount of biomedical signal data generated. The popularity of standards, such as HL7 FHIR for interoperability and data transfer, have also resulted in their use as a data storage model, which is inefficient. This article raises concern about the inefficiency of using FHIR for storage of biomedical signals and instead highlights the possibility of a sustainable storage based on data compression. Most reported efforts have focused on ECG signals; however, many other typical biomedical signals are understudied. In this article, we are considering arterial blood pressure, photoplethysmography, and respiration. We focus on simple lossless compression with low implementation complexity, low compression delay, and good compression ratios suitable for wide adoption. Our results show that it is easy to obtain a compression ratio of 2.7:1 for arterial blood pressure, 2.9:1 for photoplethysmography, and 4.1:1 for respiration.