Iceberg orders, which allow traders to hide a portion of their order size, have become prevalent in many electronic limit order markets. This paper investigates, via a real options analysis, whether small traders, who have no use for submitting iceberg orders, are better off submitting their orders to fully transparent markets which have low depth, or to more liquid markets which do permit the placement of iceberg orders by large traders. Surprisingly, we find that in the context of our model, small traders are better off submitting to fully transparent markets in spite of them being less liquid.