IGF-1 (insulin-like growth factor-1) is a hormone that is normally produced in the body in response to another hormone called growth hormone. Growth Hormone is produced by a small gland at the base of the brain (the pituitary). Together IGF-1 and GH are large contributors to growth during infancy, childhood, and adolescence. Children with IGF Deficiency are short and have an imbalance in the levels of growth hormone and IGF-1 that their body produces. Their growth hormone levels are normal or even high, but IGF-1 levels do not increase normally in response to growth hormone. As a result, they have a type of growth hormone insensitivity and an inability to grow normally. This study is a test to see whether daily dosing with a combination of rhIGF-1 and rhGH will help children with IGFD grow taller more quickly than children treated with rhGH alone. The study medications, rhIGF-1 and rhGH, are approved by the US Food and Drug Administration (FDA) for use in some growth disorders in children, but the combination of rhIGF-1 and rhGH in children with IGF-1 deficiency (IGFD) is investigational.