To address Maxgain's question about tube amp output at lower impedances: If, as Natalie and I have suggested, the tube amp's output transformer's output impedance is well-matched to the speaker load, a good tube amp should be able to output an equal, or somewhat greater, amount of power into a lower impedance speaker load, but will not be capable of "doubling down" as some SS amps can accomplish. HOWEVER, be they tube or SS, ALL amps are limited by their power supplies when it comes to their ultimate current output capabilities.
This is why 2001impala's explanation above is unfortunately a bit too simplistic. A better way to look at the situation is that a nomimal 4-ohm speaker DEMANDS more current (about twice as much) from an amplifier to reproduce the same signal as a nominal 8-ohm speaker would. Current output capability is not the strongest point of either smaller tube amps in general (tubes being better at voltage gain than current gain), or of small integrateds in general (which usually feature a shared power supply for the amp and preamp sections, and usually not a terribly large one at that). Hence, 8-ohm speakers are often recommended for moderately powered tube amplifiers, and this should help explain why the SS Yamaha could go louder in comparision (but did it sound as good?!).
Still, as long as you are using the correct output taps on the amp, I doubt you have created a serious mismatch with your amp and speakers here. Rather, I think Maxgain's points about room size, and what exactly constitutes "loud" to you, are very well-taken. You MAY have a slight mismatch on your hands between your system, your room, and your listening preferences. Despite Natalie's misgivings, Elevick and Maxgain are entirely correct when they state that adding a powered subwoofer (doesn't have to be a Velodyne) will extend system headroom, PROVIDED:
1) The sub must be run crossed-over to the speakers, rather than simply supplementing their full-range output.
2) For the amp as well as the speakers to be relieved of the power-sucking bass-reproduction duties, the crossover will have to be implemented at line-level (between the preamp and amp), rather than at the speaker level (between the amp and the speakers). This will require that your integrated feature preamp out/amp in jacks - something many integrateds lack - and for the subwoofer to be designed to operate in this manner, which most subs are not (they lack the external crossover). (For more info on this type of setup, you might want to visit the Vandersteen website and read the links pertaining to use of their 2Wq subwoofer.)
However, although such a set-up will accomplish the increased dynamic capability you desire, I am not necessarily recommending it, as the odds are actually rather iffy that the result will SOUND as good as running the system straight-up the way you presently are. Integrating a subwoofer successfully into your system in the manner I refer to above, especially when it will have to be run fairly high up in frequency to have a beneficial effect on your amp and speakers' dynamic capabilities, can be extremely difficult, and may not be worth the expense or trouble as opposed to just upgrading your speakers and amp eventually. It CAN be done in certain cases, but there are no guarantees - most audiophiles who use a sub prefer it to just supplement the extreme low-end of the spectrum while still employing true full-range speakers which are run that way (not crossed-over), a solution that can potentially benefit the sound quality, but not the system's dynamic capability.
Both your amp and your speakers are best suited for small to medium rooms, and neither qualifies as headbanger material. If you feel that you have achieved a step-up in sound quality with the Rogue amp, and are not a headbanger with a large listening room, then my first suggestion would be just enjoy it within its limits, and learn to listen at a slightly lower volume if need be. One possibly helpful approach, though, is contained on the Audio Physic website. If you don't already have your speakers set up to listen in the nearfield, this is what AP happens to recommend. The farther away you sit, the more power is needed to achieve the same apparent volume. AP speakers, unlike many others, are actually designed to be listened to close up. Their website details the particulars, and if you haven't tried this already, doing so should result in an increase in perceived volume capability. Best of luck, and happy listening!
This is why 2001impala's explanation above is unfortunately a bit too simplistic. A better way to look at the situation is that a nomimal 4-ohm speaker DEMANDS more current (about twice as much) from an amplifier to reproduce the same signal as a nominal 8-ohm speaker would. Current output capability is not the strongest point of either smaller tube amps in general (tubes being better at voltage gain than current gain), or of small integrateds in general (which usually feature a shared power supply for the amp and preamp sections, and usually not a terribly large one at that). Hence, 8-ohm speakers are often recommended for moderately powered tube amplifiers, and this should help explain why the SS Yamaha could go louder in comparision (but did it sound as good?!).
Still, as long as you are using the correct output taps on the amp, I doubt you have created a serious mismatch with your amp and speakers here. Rather, I think Maxgain's points about room size, and what exactly constitutes "loud" to you, are very well-taken. You MAY have a slight mismatch on your hands between your system, your room, and your listening preferences. Despite Natalie's misgivings, Elevick and Maxgain are entirely correct when they state that adding a powered subwoofer (doesn't have to be a Velodyne) will extend system headroom, PROVIDED:
1) The sub must be run crossed-over to the speakers, rather than simply supplementing their full-range output.
2) For the amp as well as the speakers to be relieved of the power-sucking bass-reproduction duties, the crossover will have to be implemented at line-level (between the preamp and amp), rather than at the speaker level (between the amp and the speakers). This will require that your integrated feature preamp out/amp in jacks - something many integrateds lack - and for the subwoofer to be designed to operate in this manner, which most subs are not (they lack the external crossover). (For more info on this type of setup, you might want to visit the Vandersteen website and read the links pertaining to use of their 2Wq subwoofer.)
However, although such a set-up will accomplish the increased dynamic capability you desire, I am not necessarily recommending it, as the odds are actually rather iffy that the result will SOUND as good as running the system straight-up the way you presently are. Integrating a subwoofer successfully into your system in the manner I refer to above, especially when it will have to be run fairly high up in frequency to have a beneficial effect on your amp and speakers' dynamic capabilities, can be extremely difficult, and may not be worth the expense or trouble as opposed to just upgrading your speakers and amp eventually. It CAN be done in certain cases, but there are no guarantees - most audiophiles who use a sub prefer it to just supplement the extreme low-end of the spectrum while still employing true full-range speakers which are run that way (not crossed-over), a solution that can potentially benefit the sound quality, but not the system's dynamic capability.
Both your amp and your speakers are best suited for small to medium rooms, and neither qualifies as headbanger material. If you feel that you have achieved a step-up in sound quality with the Rogue amp, and are not a headbanger with a large listening room, then my first suggestion would be just enjoy it within its limits, and learn to listen at a slightly lower volume if need be. One possibly helpful approach, though, is contained on the Audio Physic website. If you don't already have your speakers set up to listen in the nearfield, this is what AP happens to recommend. The farther away you sit, the more power is needed to achieve the same apparent volume. AP speakers, unlike many others, are actually designed to be listened to close up. Their website details the particulars, and if you haven't tried this already, doing so should result in an increase in perceived volume capability. Best of luck, and happy listening!