Question on relationship between drift velocity and resistance

Main Question or Discussion Point

Is there a relationship (or equation) between a charge carrier's drift velocity through a conducting material and that material's resistance? I'm trying to reconcile the idea that drift speeds are bigger when cross sections are smaller and the idea that resistance is bigger when cross sections are smaller. How can the drift speed be faster in smaller cross sections when resistance is bigger? I have this idea that drift speeds are proportional to current and inversely proportional to resistance. Am I right?