You could try Mind Sculpt, Tome Scour, Dream Twist, or Jace's Erasure. They would be good for mill as well if you're on a budget.

Memory Sluice is a good card for one blue mana, letting you copy it by tapping unneeded defenders. Curse of the Bloody Tome is another good passive mill card as well as Chronic Flooding.

I had Memory Sluice, but I cut them for Aqueous Form. I found it hard to get two creatures to tap, they're usually needed to block. I haven't tried Curse of the Bloody Tome, but I feel the cost is somewhat high. I will try some out though.

I wouldn't use the curse if you have access to Sphinx's Tutelage, since it does the same thing except a little better. Also, I'd put in some black. There's a lot of heavy duty mill in dimir, such as Mind Funeral, Breaking and for your zombies, Diregraf Captain. Also, I'd swap the Mind Spring for Fascination since Fascination makes both players draw, which you can combo off of the tutelage to make them mill twice that many cards, then they would draw that many, which could be a major pain in the rear, if not a finishing move.

My mill isn't modern, but I run Spoils of Evil to go along with something like that, Mind Grind or Keening Stone as a finishing move. If you're not playing competitively, that might help some if you can find it, along with Guiltfeeder.

Traumatize is another solid option, no matter what type of mill you run, though.

Considering most the dimir mill cards break the bank, I can't implement them really. I'm wanting to make this as competitive as possible, so I don't think I can add the other cards you suggested such as Spoils of Evil. The main focus is Undead Alchemist, and games are usually over by turn 5-6 with it, so I wont even have a use for Keening Stone. I tried using traumatize, but it usually added up as a dead card, and by turn 5, only mills 10-15 cards. Thank you for the suggestion of Fascination, I will consider it. I'm not sure I like the idea of giving my opponent card draw or mill myself though, but I will think about it and test it. Thanks again for all the suggestions. Any clue on what to do about the sideboard? I'm thinking of adding green in for more protection and ramp to surprise opponents round two.

Because you run tutelage, when it's out, Fascination basically just reads XUU: Each player draws X cards, because when you combine the two, magic happens.

Say lategame you have 8 mana sitting on board, Tutelage is stuck, and you've got no reason to fear counterspells. Just tap it all for Fascination and have both of you draw 6. This also causes 6 triggers of Sphinx's Tutelage. So if you consider the 6 you made them draw as mill (you should), you've hit them for a minimum of 18 cards in one move, 20 for the turn with draw step, and likely many more. Considering the game plan, this likely means you win as soon as you say "pass turn".

Fascination isn't so much a staple every play card, it's essentially your big finisher that combos with Sphinx's Tutelage to finish the game, or at least get damn close.

Skybane, I hadn't thought about it like that. It would be perfect for a late game finisher. Thanks for the advice, I'll find a way to implement it. Any suggestions on the sideboard?

I really recommend Traumatize here, I know it's a budget build, but it will make this deck waaaaay better!

I initially stated Traumatize was usually pointless, because I would use the mana to get out combo pieces. The deck does have a tendency to run slow though, so I will attempt to implement them. thank you for the suggestion

I see you're more of stitcher than a ghoul caller. You'd probably like Thought Scour for it's synergy with Sphinx's Tutelage and making Jace's Phantasm more playable early on, which I would play more of. You're much more likely to win with a 5/5 flyer than a Ludevic's Test Subject  ^Flip. Most opponents will let you invest a bunch of mana and Lightning Bolt when then need to (or win, which ever comes first).

I had forgotten I had cut out Thought Scour, that has perfect synergy, thank you. And from playtesting this deck, you're right about Jace's Phantasm. He's just more expensive. But I think that will work better in the long run. Thank you for the advice

I know you said Dimir tends to be more pricy, but some things you want to consider, especially playing the format you are now:

Breaking is running about .50 right now. It's a very substantial mill card for pretty low CMC.

You'll get access to things like Wight of Precinct Six (Which is a zombie that gets huge. about .20 right now) and effective removal spells like Dismember (Pricier side being about $1) or Doom Blade (about .40). Stalling with Psychic Strike (about .20)

Just some things to consider. Btw, Geralf's Mindcrusher is super slow, but super fun to play with, as his ability goes off twice with Undying :P

Tormentero, I've tried multiple times to break into Dimir, but I always end up losing out on the consistency of the combo. I'll post a link to the best deck I've built after I tweak it a bit to show you what I mean. And thanks for the tip on Geralf's Mindcrusher.

No supporting zombies for Undead Alchemist?

I have found that usually when I put him out, he generates all the zombies I could ever want. Any time I add one, it just messes with the focus. If you think of any blue zombies that may help though, I'll be glad to here it, and definitely consider using them

Consuming Aberration if you wanna do some black

Consuming Aberration is no good in the deck, it's a horror, and it can't be played until turn 5, usually the turn the game is over. Also, I've tried multiple times to make a dimir version of this deck, and it always looses consistency. Thank you for the suggestion though.

Archive Trap + Ghost Quarter Usually a staple in mills

I would implement that combo, but Archive Trap is no where near my budget. I would trade it out for Traumatize, and get rid of two Halimar Depths for Ghost Quarter. Thank you for the suggestion. Any advice on the sideboard?

Sideboard for mill decks is mostly about graveyard management(geared since your mono blue and budget)-

Relic of Progenitus/Tormod's Crypt- you need a way to clear a graveyard so shuffle triggers don't kill you.
Grafdigger's Cage- keeps people from using the grave as a large hand.
Pithing Needle- keeps troublsome creature ability and planewalkers in check
Torpor Orb- helps with twin/ decks that like to abuse etb triggers.
Hurkyl's Recall - bounces artifacts back: useful against tron/affinity
Monastery Siege/Witchbane Orb/Orbs of Warding- to help with burn
Glaring Spotlight- boggles and can help with burn/removal
Cyclonic Rift- good one sided boardwipe or to just bounce a problem early game

Also note that most of these cards are 1 cmc artifacts allowing Trinket Mage to tutor for them so 1 or 2 in the board becomes 5 or 6 main with trinket trigger

Your main board can definetly handle 4 Ghost Quarter which help deal with tron lands, man/ utility lands

1. What is you budget on cards- ex: >$5?
   

Thank you so much for the help, I'be tried to keep the deck $30, but to make competitive I'll be willing to pay a bit more. Definitely nothing over $5 per card though. Do you think Halimar Depths is worth it, or should I trade them for the Ghost Quarter? I'm trying to make this deck as efficient as possible. I really like the artifacts you suggested, and I'll try and implement them. Anything you see in my mainboard that's slowing me down?

I just realized, Torpor Orb would break my deck, because my deck is based on ETB with Altar of the Brood

Profane Memento i used it in standard mill when origins came out. thought it was useful with tutelage at the time.

Mind Sculpt dirt cheap, not instant though

Radiant Fountain - useful vs burn, great if running mono color and not devotion based.

Dakra Mystic - slightly useful

Profane Memento might be useful, since I can tutor it, and Radiant Fountain might be nice too. I've used the other two in the past, they just didn't help enough in the long run

Profane Memento might be useful, since I can tutor it, and Radiant Fountain might be nice too. I've used the other two in the past, they just didn't help enough.