Avenues for getting ~$1M funding in India

I am curious about opportunities to get funding in the $1M range for start-ups in India.

1. Most of the VCs in India seem to be interested only in deals over $2M. The average size seems to be $4M-5M. I believe this is a direct consequence of VCs raising funds over $100M. Even if you write $5M checks you still need to manage 20 companies! So cannot afford to make and then manage small investments. Also, with the valuations of many established companies falling to ground levels, with a $5-10M investment, VCs can now get a good stake at low risk. So more VCs seem to be doing PE type deals.
2. $1M is still a big amount in India. It cannot be raised from Friends, family and fools. Angel investors also balk at that number. Are there any professional investors who fund in this range? What are the options available for companies planning to raise in this range? (Of course, if there are no options available, we can always wait till we have greater investment needs)