1. Use any just and reasonable method of determining the extent of an improvement district consistent with the benefits derived;

2. Use any just and reasonable method of apportioning the sum to be assessed among the properties determined to be specially benefited; and

3. Authorize payment by the city of all or part of the cost of the improvement when, in the opinion of the council, the topographical or physical conditions, or unusual or excessive public travel, or other character of the work involved warrants only a partial payment or no payment of the total costs of the improvement by the benefited property.