In an embodiment, an apparatus includes a consuming logic to request and process data including a critical data portion and a second data portion, the data stored in a memory coupled to a processor interposed between the apparatus and the memory. In addition, the apparatus includes a protocol stack logic coupled to the consuming logic to issue a read request to the memory via the processor to request the data and to receive a plurality of completions responsive to the read request. In an embodiment, the protocol stack logic includes a completion handling logic to send data of a first of the completions to the consuming logic before protocol stack processing is completed on the completions. Other embodiments are described and claimed.