Modern processors, e.g., Intel SGX, allow applications to isolate secret code and data in encrypted memory regions called enclaves. While encryption effectively hides the contents of memory, the sequence of address references issued by the secret code leaks information. This is a serious problem because these leaks can easily break the confidentiality guarantees of enclaves. In this paper, we explore Oblivious RAM (ORAM) designs that prevent these information leaks under the constraints of modern SGX processors. Most ORAMs are a poor fit for these processors because they have high constant overhead factors or require large private memories, which are not available in these processors. We address these limitations with a new hierarchical ORAM construction, the Pyramid ORAM, that is optimized towards online bandwidth cost and small blocks. It uses a new hashing scheme that circumvents the complexity of previous hierarchical schemes. We present an efficient x64-optimized implementation of Pyramid ORAM that uses only the processor's registers as private memory. We compare Pyramid ORAM with Circuit ORAM, a state-of-the-art tree-based ORAM scheme that also uses constant private memory. Pyramid ORAM has better online asymptotical complexity than Circuit ORAM. Our implementation of Pyramid ORAM and Circuit ORAM validates this: as all hierarchical schemes, Pyramid ORAM has high variance of access latencies; although latency can be high for some accesses, for typical configurations Pyramid ORAM provides access latencies that are 8X better than Circuit ORAM for 99% of accesses. Although the best known hierarchical ORAM has better asymptotical complexity, Pyramid ORAM has significantly lower constant overhead factors, making it the preferred choice in practice.