Recommendation for efficient and smooth razor

I think I have to just try some different ones, that's where the BST comes in handy.
   I'm thinking maybe titanium might help you but there's the price cap you put on it. 
   Possibly a blackbird or something from blackland razors maybe the vector like somebody said already.
   Somebody above also mentioned lupo .95.
    Possibly some kind of adjustable to find your range.
   You know I think most of us wet shavers go to this.

For smooth, efficient and lack of nicks I’d suggest the Maggard SS70 or RazoRock Mamba 70…. They’re sort of the same thing with cosmetic differences. Both well under $100.

Based on your post, I’d recommend the Yates H plate on the less expensive side but if you want to get something special and within your budget, I’d go with a Wolfman WR2 (head only) in basic polish and just use one of your existing handles.

With the conversion from CAD to USD you should still fall within your budget.

Check out the Wolfman WR2 thread to get a better idea on what gap or gap combo that you think best fits you.

Let us know what you decide!

The Karve Overlander has become one of the top "efficient but smooth daily drivers" for me. And it is well under your budgeted amount. The Rockwell 6S (plates 4 and 5) is also a fantastic daily driver.

Winner!

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$250 Budget

Rockwell 6s 
Carbon 
Charcoal Goods Level 2
Timeless Polished Ti Slim with Crown Handle

My recommendation is the Rockwell 6s.  Its a modern razor, its smooth and as efficient as you want depending on the plate you select from 1 through 6.  I use plate 3 or 4 with a Feather as a daily shaver and will occasionally venture into 5/6 territory if I want a little more aggressiveness or, 2 if Im unwilling to focus too much.  I've never tried plate 1 but I think it would probably give an acceptable shave.

Over the course of time the Rockwell 6s is clearly a winner, There’s something in that box for everyone!

My recommendation is the Rockwell 6s.  Its a modern razor, its smooth and as efficient as you want depending on the plate you select from 1 through 6.  I use plate 3 or 4 with a Feather as a daily shaver and will occasionally venture into 5/6 territory if I want a little more aggressiveness or, 2 if Im unwilling to focus too much.  I've never tried plate 1 but I think it would probably give an acceptable shave.

Over the course of time the Rockwell 6s is clearly a winner, There’s something in that box for everyone!

That would sure help to nail down how efficient of a razor you are after. Can't go wrong on the price, you would have some budget left.

Overlander and Yates M would be great choices.

I have to root for the Henson AL13 Mild. - $89.99 CAD

The most impressive thing I found with mine is the precision of the machining. An example that is when you go to screw the head onto the handle, after 1 or 2 turns there is very little "wobble" in the handle-to-head connection. Most razors have lots of wiggle room right up until it comes up against the base plate. Even so, both the handle and the head can fit other brands of 5 mm heads and handles.

Also, the head is something like a millimetre longer than a blade (so no risk of scratches from the blade ends), yet it's close enough to the ends that it's still easy to safely pick a blade up off the head.

It's the quietest of any razor I've tried, because there's no blade chatter. I remember that the third time I used it I had to stop mid-pass and make sure I had actually put a blade in it. (I did.)

The handle is a bit longer than I usually like but being made of aluminum, the mass and balance is perfect for me.

Handle dimensions
The handle is tapered from 12.25 mm [.482”] at the tail to 9.75 mm [.384”] near the head.
The overall handle length is 96 mm [3.780”].

Weight:
Henson AL13 - 1.3oz (36.9 g) - including the head
Henson Ti22 - 2.7oz (76.5 g)

They have several other colours besides "Rocket Red", plus you can request different-coloured parts in the same razor, if you describe the combination in the "Special instructions for seller" form just before the checkout.

They don't actually call it the "mild" model, but there's another more aggressive AL13 that they do call "Medium"
It feels mild enough that I can now safely use new Feather blades, but I'll use a couple of different blades in it - Feather, Astra SP, Shaverboy, and Derby Extra.
(I still don't like Wilkinson Sword blades though. They feel rough to me in any razor.)

Technical Details
AL13 - .68 mm [.027”] Blade Gap and .033 mm [.0013"] Blade Exposure
AL13 - Medium - .85 mm [.033”] Blade Gap and .058 mm [.0023”] Blade Exposure

My AL13 Mild feels similar to a Gillette Slim set to "3" (but does a better job of shaving).

There is also the "Ti22", in titanium, and in three different levels of aggression, for $321.43 CAD.

I think it as my “mild, smooth but efficient" king.  Of all the razors I've ever tried (including most of those already mentioned in this thread) the Haircut & Shave N075 mixed metal wins (at least for me) for being supremely easy and yet giving a close shave. It’s decidedly not aggressive, in fact, it’s quite mild.  If you you want efficiency first, it might be too much so. I own two - can never be without one.  And $190 is a great price for this well made shaver.