Ad-hoc radio networks and multiple access channels are classical and well-studied models of distributed systems, with a large body of literature on deterministic algorithms for fundamental communications primitives such as broadcasting and wake-up. However, almost all of these algorithms assume knowledge of the number of participating nodes and the range of possible IDs, and often make the further assumption that the latter is linear in the former. These are very strong assumptions for models which were designed to capture networks of weak devices organized in an ad-hoc manner. It was believed that without this knowledge, deterministic algorithms must necessarily be much less efficient. In this paper we address this fundamental question and show that this is not the case. We present \emph{deterministic} algorithms for \emph{blind} networks (in which nodes know only their own IDs), which match or nearly match the running times of the fastest algorithms which assume network knowledge (and even surpass the previous fastest algorithms which assume parameter knowledge but not small labels). Specifically, in multiple access channels with $k$ participating nodes and IDs up to $L$, we give a wake-up algorithm requiring $O(\frac{k\log L \log k }{\log\log k})$ time, improving dramatically over the $O(L^3 \log^3 L)$ time algorithm of De Marco et al. (2007), and a broadcasting algorithm requiring \sloppy{$O(k\log L \log\log k)$ }time, improving over the $O(L)$ time algorithm of Gasieniec et al. (2001) in most circumstances. Furthermore, we show how these same algorithms apply directly to multi-hop radio networks, achieving even larger running time improvements.