  We constrain slow-roll inflationary models using the recent WMAP data
combined with data from the VSA, CBI, ACBAR and 2dF experiments. We find the
slow-roll parameters to be $0 < \epsilon_1 < 0.032$ and $\epsilon_2 + 5.0
\epsilon_1 = 0.036 \pm 0.025$. For inflation models $V \propto \phi^{\alpha}$
we find that $\alpha< 3.9, 4.3$ at the 2$\sigma$ and $3\sigma$ levels,
indicating that the $\lambda\phi^4$ model is under very strong pressure from
observations. We define a convergence criterion to judge the necessity of
introducing further power spectrum parameters such as the spectral index and
running of the spectral index. This criterion is typically violated by models
with large negative running that fit the data, indicating that the running
cannot be reliably measured with present data.
