A Rental agreement is a contract between a landlord and a tenant; a lease is a form of rental agreement.
The Ohio Landlord Tenant Law says this about rental agreements
1. Everyone has a rental agreement 2. Landlords may include a landlord's duty into a tenants rental agreement 3. There are specific terms barred from rental agreements 4. A rental agreement may not be unconscionable. 5. Tenants have the right to bargain collectively on the terms and conditions of the rental agreement (5321.02)
Here's some terms of a lease that might work for you.
Terminate on death or disability
Terminate on change of job
Energy Savings improvements
Longer term, smaller increase
October 18, 2016 Go Banking Rates has two good stories on negotiating a better deal Maybe these stories could make you into a smarter housing consumers.