We study an auction design problem where a seller aims to sell a single item to multiple bidders with independent private values. The seller knows only an upper bound on these values and does not know their distribution. The objective is to devise a deterministic auction mechanism effective across a broad set of distributions. We propose a second-price auction with a reserve price set at half of the upper bound. Even though no deterministic mechanism can achieve a positive fraction of the maximum achievable expected revenue across all distributions, we show that our mechanism achieves at least 1/4 ( 1/2 under i.i.d. values) of the maximum expected revenue for a broad range of distributions of practical importance. Numerical experiments under randomly generated distributions demonstrate the superior performance of our mechanism in approximately 95% of the generated instances compared to benchmark mechanisms from the literature. We also account for errors in the upper bound estimate. Our deterministic mechanism is simple, requires minimal information, and is provably effective in various practical scenarios.