CAML Query for getting folder contents based on folder parameters

I have the following folder structure.

Folder1 attr1="cat1"
>>  file1 attr2="subcat1"
>>  file2 attr2="subcat2"
Folder2 attr1="cat2"
>>  file3 attr2="subcat1"
>>  file4 attr2="subcat2"
Folder3 attr1="cat1"
>>  file5 attr2="subcat1"
>>  file6 attr2="subcat2"

I want to get all files(only) which is under folder having field attr1 = cat1, i.e., file1, file2, file5, and file6. Note that attr1 is not available for files. A possible solution is to get all folders, then in a loop, query for files using FolderServerRelativeUrl. But I don't think it is optimal because there will be too much delay for the retrieving the final list, as each ExecuteQuery will take some time. I am using Client Object Model for querying. The CAML query I use only retrieves Folders at Present.

string caml = @"<View Scope='RecursiveAll'>
                            <Query>
                                <Where>
                                    <And>
                                        <Eq>
                                            <FieldRef Name='attr1' />
                                            <Value Type='Text'>cat1</Value>
                                        </Eq>
                                    </And>
                                </Where> 
                            </Query>
                        </View>";