(hyper)sensitivity of goodness-of-fit tests

I have a large amount of empirical data consisting of interarrival
times that I believe are exponentially distributed. Looking at the
quantile-quantile plot between the empirical and theoretical/fitted
distribution, I see an almost perfect linear relationship.

However, if I conduct a chi-square test, or kolmogorow-smirnov test,
the tests strongly reject the hypothesis that the interarrival times
are exponentially distributed. It seems that these tests are "too
sensitive" for large data sets. (In our case, we have over 1.5 million
interarrival data points.) Are there standard techniques for applying
goodness-of-fit tests to large pools of empirical data to make them
less senstive to arguably insignificant and minor discrepencies between
real-world data and a theoretical distribution? Thanks very much for
any help.

(Below I give an example of what happens with a chi-square test.

For example:

interval length empirical expected chi-square
summand

0-2 927,256 911,012.88 289.61
2-4 397,959 413,849.31 610.13
4-6 181,593 188,000.92 218.41
6-8 85,075 85,403.90 1.27
8-10 40,289 38,796.76 57.40
10-12 18,914 17,624.35 94.37
12-14 9,443 8,006.28 257.82
14-16 4,510 3,637.04 209.52
16-18 2,185 1,652.21 171.81
18-20 1,037 750.56 109.32
20 1,098 624.78 358.43

totals: 1669359 1669359.00 2378.07

Looking at a chi-square table, with 10 degrees of freedom from 11 bins,
we reject the null hypothesis that the interarrival lengths follow an
exponential distribution.)

.

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