We present a Monte Carlo study of the correlation length xi of randoml
y diluted antiferromagnetic spin-1/2 two-chain Heisenberg ladders with
weak and intermediate interchain couplings, J/J less than or equal to
1. We are able to access the experimentally relevant low-temperature
regime, T/J approximate to 1/500, and find (i) that the form xi(z, T)
= A(z) + B(z)T-v, with v = 0.40(5), describes our data at low and mode
rate dilution z and up to rather high temperatures, (ii) evidence for
scaling of xi J/J in the variable zJ/J at weak J/J, (iii) an enhanceme
nt of correlations that is strongest for a fraction z approximate to J
/(8J) of dilutants, and (iv) that the Neel temperature of Sr(Cu1-xZnz)
(2)O-3 corresponds well to a curve of constant correlation length xi =
18(2) of the single diluted ladder with J/J less than or equal to 1/2
.