Colour me stupid, but is there something to prevent inserting indeterminate padding while sending headers? e.g. imagine a request like GET / HTTP/1.0 X

Colour me stupid, but is there something to prevent inserting indeterminate padding while sending headers? e.g. imagine a request like GET / HTTP/1.0 X-Pad: GET / HTTP/aaaaaaa Where X-Pad randomly repeats previous bytes, and perhaps 0..8 bytes of random/repeating variable-length data. By randomizing the effectiveness of the compression, surely this attack can be generally prevented by the browser? You could argue that given enough samples the noise could be filtered and the attack still remains, but the same could be said the same for many successful patches over the years (TCP sequence number randomization, Kaminsky's DNS issue, etc.), and the number of samples required would be pretty infeasible.