arcgis 10.1 - Concatenate only when all fields to be concatenated have values

I have two fields that I want to concatenate. Field1 contains null values and Field2 has values for every record. I want to concatenate only when both fields have values. I tried using a function with an if/else statement but that doesn't work as the resulting concatenation will return values from field2.

def concat_fields(field1, field2):
    if field1 == ""
        return 

    else:
        return field1 + field2

I know this is wrong. Any suggestions?

EDIT:

Answer

Based on your results, it looks like field1 may have a space (" ") in the field, instead of an empty string.

def concat_fields(field1, field2):
    if field1.strip() == "" or field2.strip() == "":
        return ""
    else:
        return field1 + field2