Symbolic and concolic execution find important applications in a number of security-related program analyses, including analysis of malicious code. However, malicious code tend to very often be obfuscated, and current concolic analysis techniques have trouble dealing with some of these obfuscations, leading to imprecision and/or excessive resource usage. This paper discusses three such obfuscations: two of these are already found in obfuscation tools used by malware, while the third is a simple variation on an existing obfuscation technique. We show empirically that existing symbolic analyses are not robust against such obfuscations, and propose ways in which the problems can be mitigated using a combination of fine-grained bit-level taint analysis and architecture-aware constraint generations. Experimental results indicate that our approach is effective in allowing symbolic and concolic execution to handle such obfuscations.