An inner space–time code, i.e., one that is complemented by an outer error-control code, calls for vastly different design strategies than a space–time code that stands alone. This letter investigates the design of a linear inner space–time code for a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> -input <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r$</tex> -output Rayleigh fading channel by examining its outage capacity, which assumes an idealized outer code. We show that a linear space–time code with rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R ≪ min(t, r)$</tex> can achieve at most a fraction <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R/min(t, r)$</tex> of the underlying channel's outage capacity at high signal-to-noise ratio (SNR). Conversely, we find that a space–time code with low raw diversity order (as calculated using the rank rule) does not necessarily suffer a capacity penalty. Under very general conditions, a rate of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R = min(t, r)$</tex> is sufficient to ensure that the outage capacity of the space–time code approaches that of the underlying channel at high SNR. Simulation results are presented to support the claims.