ArrayList<Item> goodItems = new ArrayList<Item>();
boolean isDone = false;

do{
    new dataTask().getMyData(new myCallback() {
       // ...some logic here...
    });
}
while(goodItems.size() < 20 || isDone != true);

private class DownloadTask extends AsyncTask<URL, Void, ArrayList<Item>> {

     boolean isDone = false;

     protected Long doInBackground(URL... urls) {

         ArrayList<Item> goodItems = new ArrayList<Item>();

         while (goodItems.size() < 20 || isDone != true) {
            // request and adding of items to goodItems
         }

         return goodItems;
     }

     protected void onPostExecute(ArrayList<Item> result) {
        // update views
     }
 }

new DownloadTask().execute("exampleurl.com/data");

MyCallback cb = new MyCallback(){
 if(goodItems.size() < 20) new DataTask().getMyData(cb);
}
new DataTask().getMyData(cb);

ArrayList<Item> goodItems = new ArrayList<Item>();

void fetchItems() {
    new dataTask().getMyData(new myCallback(){
        @Override
        public void onComplete(List<Item> items) {
            // some logic here
            if (goodItems.size() < 20 || isDone != true) {
                fetchItems();
            }
        }
    });
}

void load() {
    new DataTask().getMyData(new MyCallback() {
        void onComplete(List<Item> items) {
            goodItems.addAll(items);
            if (goodItems.size() < 20) {
                load();
            }
    });
}