diff --git a/benchpress.opam b/benchpress.opam
index 736d246..bf911c9 100644
--- a/benchpress.opam
+++ b/benchpress.opam
@@ -21,6 +21,7 @@ depends: [
   "uuidm"
   "base64"
   "ptime"
+  "processor"
   "pp_loc" { >= "2.0" & < "3.0" }
   "gnuplot" { >= "0.6" & < "0.8" }
   "sqlite3"
diff --git a/src/bin/Run_main.ml b/src/bin/Run_main.ml
index 3ef177d..cc3c3d2 100644
--- a/src/bin/Run_main.ml
+++ b/src/bin/Run_main.ml
@@ -3,16 +3,17 @@ module T = Test
 module Log = (val Logs.src_log (Logs.Src.create "benchpress.run-main"))
 
 (* run provers on the given dirs, return a list [prover, dir, results] *)
-let execute_run_prover_action ?j ?timestamp ?pp_results ?dyn ?limits ?proof_dir
-    ?output ~notify ~uuid ~save ~wal_mode ~update (defs : Definitions.t)
-    (r : Action.run_provers) : _ * Test_compact_result.t =
+let execute_run_prover_action ?j ?cpus ?timestamp ?pp_results ?dyn ?limits
+    ?proof_dir ?output ~notify ~uuid ~save ~wal_mode ~update
+    (defs : Definitions.t) (r : Action.run_provers) : _ * Test_compact_result.t
+    =
   Error.guard
     (Error.wrapf "run prover action@ `@[%a@]`" Action.pp_run_provers r)
   @@ fun () ->
   let interrupted = CCLock.create false in
   let r =
-    Exec_action.Exec_run_provers.expand ?dyn ?j ?proof_dir ?limits defs r.limits
-      r.j r.pattern r.dirs r.provers
+    Exec_action.Exec_run_provers.expand ?dyn ?j ?cpus ?proof_dir ?limits defs
+      r.limits r.j r.pattern r.dirs r.provers
   in
   let len = List.length r.problems in
   Notify.sendf notify "testing with %d provers, %d problems…"
@@ -68,7 +69,7 @@ type top_task =
   | TT_run_slurm_submission of
       Action.run_provers_slurm_submission * Definitions.t
 
-let main ?j ?pp_results ?dyn ?timeout ?memory ?csv ?(provers = []) ?meta:_
+let main ?j ?cpus ?pp_results ?dyn ?timeout ?memory ?csv ?(provers = []) ?meta:_
     ?summary ?task ?(dir_files = []) ?proof_dir ?output ?(save = true)
     ?(wal_mode = false) ~desktop_notification ~no_failure ~update
     ?(sbatch = false) ?partition ?nodes ?addr ?port ?ntasks
@@ -188,7 +189,7 @@ let main ?j ?pp_results ?dyn ?timeout ?memory ?csv ?(provers = []) ?meta:_
 
     let top_res, (results : Test_compact_result.t) =
       execute_run_prover_action ~uuid ?pp_results ?proof_dir ?dyn:progress
-        ~limits ?j ?output ~notify ~timestamp ~save ~wal_mode ~update defs
+        ~limits ?j ?cpus ?output ~notify ~timestamp ~save ~wal_mode ~update defs
         run_provers_action
     in
     if CCOpt.is_some csv then (
diff --git a/src/bin/benchpress_bin.ml b/src/bin/benchpress_bin.ml
index 145fd21..5c36aef 100644
--- a/src/bin/benchpress_bin.ml
+++ b/src/bin/benchpress_bin.ml
@@ -19,8 +19,8 @@ module Run = struct
   (* sub-command for running tests *)
   let cmd =
     let open Cmdliner in
-    let aux j pp_results dyn paths dir_files proof_dir defs task timeout memory
-        meta provers csv summary no_color output save wal_mode
+    let aux j cpus pp_results dyn paths dir_files proof_dir defs task timeout
+        memory meta provers csv summary no_color output save wal_mode
         desktop_notification no_failure update =
       catch_err @@ fun () ->
       if no_color then CCFormat.set_color_default false;
@@ -30,8 +30,8 @@ module Run = struct
         else
           None
       in
-      Run_main.main ~pp_results ?dyn ~j ?timeout ?memory ?csv ~provers ~meta
-        ?task ?summary ~dir_files ?proof_dir ?output ~save ~wal_mode
+      Run_main.main ~pp_results ?dyn ~j ?cpus ?timeout ?memory ?csv ~provers
+        ~meta ?task ?summary ~dir_files ?proof_dir ?output ~save ~wal_mode
         ~desktop_notification ~no_failure ~update defs paths ()
     in
     let defs = Bin_utils.definitions_term
@@ -51,8 +51,7 @@ module Run = struct
       Arg.(value & flag & info [ "wal" ] ~doc:"turn on the journal WAL mode")
     and dir_files =
       Arg.(
-        value
-        & opt_all file []
+        value & opt_all file []
         & info [ "F" ] ~doc:"file containing a list of files")
     and proof_dir =
       Arg.(
@@ -67,6 +66,47 @@ module Run = struct
         & opt (some int) None
         & info [ "t"; "timeout" ] ~doc:"timeout (in s)")
     and j = Arg.(value & opt int 1 & info [ "j" ] ~doc:"level of parallelism")
+    and cpus =
+      let doc =
+        "Limit the specific CPUs or cores to use. When provided, the\n\
+        \      [-j] flag is ignored, and each prover gets allocated its own \
+         CPU core from\n\
+        \      this list. A comma-separated list or hyphen-separated ranges \
+         are allowed."
+      in
+      let parser s =
+        match String.split_on_char '-' s with
+        | [] -> assert false (* [split_on_char] invariant *)
+        | [ n ] -> Result.map (fun x -> x, x) Arg.(conv_parser int n)
+        | [ n; m ] ->
+          Result.bind Arg.(conv_parser int n) @@ fun n ->
+          Result.bind Arg.(conv_parser int m) @@ fun m ->
+          if m < n then
+            Error (`Msg (Format.asprintf "invalid range: %d-%d" n m))
+          else
+            Ok (n, m)
+        | _ -> Error (`Msg (Format.asprintf "invalid cpuset: %s" s))
+      in
+      let printer ppf (n, m) =
+        if n = m then
+          Format.pp_print_int ppf n
+        else
+          Format.fprintf ppf "%d-%d" n m
+      in
+      let cpuspec = Arg.conv ~docv:"MASK" (parser, printer) in
+      let parse xs =
+        let cpus =
+          CCList.flat_map
+            (fun (n, m) -> List.init (m + 1 - n) (fun i -> i + n))
+            xs
+          |> List.sort_uniq Int.compare
+        in
+        match cpus with
+        | [] -> None
+        | _ -> Some cpus
+      in
+      Term.(
+        const parse $ Arg.(value & opt (list cpuspec) [] & info [ "cpus" ] ~doc))
     and memory =
       Arg.(
         value
@@ -123,9 +163,10 @@ module Run = struct
     in
     Cmd.v (Cmd.info ~doc "run")
       Term.(
-        const aux $ j $ pp_results $ dyn $ paths $ dir_files $ proof_dir $ defs
-        $ task $ timeout $ memory $ meta $ provers $ csv $ summary $ no_color
-        $ output $ save $ wal_mode $ desktop_notification $ no_failure $ update)
+        const aux $ j $ cpus $ pp_results $ dyn $ paths $ dir_files $ proof_dir
+        $ defs $ task $ timeout $ memory $ meta $ provers $ csv $ summary
+        $ no_color $ output $ save $ wal_mode $ desktop_notification
+        $ no_failure $ update)
 end
 
 module Slurm = struct
@@ -169,8 +210,7 @@ module Slurm = struct
       Arg.(value & flag & info [ "wal" ] ~doc:"turn on the journal WAL mode")
     and dir_files =
       Arg.(
-        value
-        & opt_all file []
+        value & opt_all file []
         & info [ "F" ] ~doc:"file containing a list of files")
     and proof_dir =
       Arg.(
diff --git a/src/core/Exec_action.ml b/src/core/Exec_action.ml
index 7740229..ffb3327 100644
--- a/src/core/Exec_action.ml
+++ b/src/core/Exec_action.ml
@@ -5,9 +5,10 @@ module Log = (val Logs.src_log (Logs.Src.create "benchpress.runexec-action"))
 
 module Exec_run_provers : sig
   type t = Action.run_provers
+  type jobs = Bounded of int | Cpus of int list
 
   type expanded = {
-    j: int;
+    j: jobs;
     problems: Problem.t list;
     provers: Prover.t list;
     checkers: Proof_checker.t Misc.Str_map.t;
@@ -18,6 +19,7 @@ module Exec_run_provers : sig
   val expand :
     ?slurm:bool ->
     ?j:int ->
+    ?cpus:int list ->
     ?dyn:bool ->
     ?limits:Limit.All.t ->
     ?proof_dir:string ->
@@ -73,6 +75,7 @@ module Exec_run_provers : sig
     Test_top_result.t lazy_t * Test_compact_result.t
 end = struct
   type t = Action.run_provers
+  type jobs = Bounded of int | Cpus of int list
 
   let ( >? ) a b =
     match a with
@@ -85,7 +88,7 @@ end = struct
     | Some _ as x -> x
 
   type expanded = {
-    j: int;
+    j: jobs;
     problems: Problem.t list;
     provers: Prover.t list;
     checkers: Proof_checker.t Misc.Str_map.t;
@@ -136,21 +139,27 @@ end = struct
     | exn -> Error.(raise @@ of_exn exn)
 
   (* Expand options into concrete choices *)
-  let expand ?(slurm = false) ?j ?(dyn = false) ?limits ?proof_dir ?interrupted
-      (defs : Definitions.t) s_limits s_j s_pattern s_dirs s_provers : expanded
-      =
+  let expand ?(slurm = false) ?j ?cpus ?(dyn = false) ?limits ?proof_dir
+      ?interrupted (defs : Definitions.t) s_limits s_j s_pattern s_dirs
+      s_provers : expanded =
     let limits =
       match limits with
       | None -> s_limits
       | Some l -> Limit.All.with_defaults l ~defaults:s_limits
     in
     let j =
-      j >?? s_j
-      >?
-      if slurm then
-        0
-      else
-        Misc.guess_cpu_count ()
+      match cpus with
+      | None ->
+        let j =
+          j >?? s_j
+          >?
+          if slurm then
+            0
+          else
+            Misc.guess_cpu_count ()
+        in
+        Bounded j
+      | Some cpus -> Cpus cpus
     in
     let problems =
       CCList.flat_map
@@ -331,10 +340,19 @@ end = struct
     (* run provers *)
     let res_l =
       let db = CCLock.create db in
-      Misc.Par_map.map_p ~j:self.j
-        (fun (prover, pb) -> run_prover_pb ~prover ~pb ~db ())
-        jobs
-      |> CCList.flatten
+      match self.j with
+      | Bounded j ->
+        Misc.Par_map.map_p ~j
+          (fun (prover, pb) -> run_prover_pb ~prover ~pb ~db ())
+          jobs
+        |> CCList.flatten
+      | Cpus cpus ->
+        Misc.Par_map.map_with_resource ~resources:cpus
+          (fun cpu (prover, pb) ->
+            Log.debug (fun m -> m "Running on cpu %d" cpu);
+            Misc.with_affinity cpu (run_prover_pb ~prover ~pb ~db))
+          jobs
+        |> CCList.flatten
     in
 
     if interrupted () then Error.fail "run.interrupted";
@@ -375,6 +393,13 @@ end = struct
       ~port ~ntasks ?output ?(update = false) ~uuid ~save ~wal_mode
       (self : expanded) : _ * _ =
     ignore on_start_proof_check;
+    let j =
+      match self.j with
+      | Bounded j -> j
+      | Cpus cpus ->
+        Log.warn (fun m -> m "cpu affinity ignored in slurm mode");
+        List.length cpus
+    in
     let start = Misc.now_s () in
     let db =
       prepare_db ~wal_mode ?output ~update timestamp uuid save self.provers
@@ -556,7 +581,7 @@ end = struct
           (Unix.string_of_inet_addr addr)
           used_port);
     let sbatch_cmds =
-      Slurm_cmd.mk_sbatch_cmds self.limits self.proof_dir self.j addr used_port
+      Slurm_cmd.mk_sbatch_cmds self.limits self.proof_dir j addr used_port
         partition config_file nodes
     in
     let job_ids =
diff --git a/src/core/Exec_action.mli b/src/core/Exec_action.mli
index cfd0d66..b8bbef1 100644
--- a/src/core/Exec_action.mli
+++ b/src/core/Exec_action.mli
@@ -5,8 +5,13 @@ type cb_progress =
 module Exec_run_provers : sig
   type t = Action.run_provers
 
+  type jobs =
+    | Bounded of int (* [Bounded j] is at most [j] parallel jobs *)
+    | Cpus of int list
+  (* [Cpus cpus] assigns an exclusive cpu from [cpus] to each job *)
+
   type expanded = {
-    j: int;
+    j: jobs;
     problems: Problem.t list;
     provers: Prover.t list;
     checkers: Proof_checker.t Misc.Str_map.t;
@@ -17,6 +22,7 @@ module Exec_run_provers : sig
   val expand :
     ?slurm:bool ->
     ?j:int ->
+    ?cpus:int list ->
     ?dyn:bool ->
     ?limits:Limit.All.t ->
     ?proof_dir:string ->
diff --git a/src/core/Misc.ml b/src/core/Misc.ml
index 40d7aaf..eb174f6 100644
--- a/src/core/Misc.ml
+++ b/src/core/Misc.ml
@@ -317,6 +317,34 @@ module Par_map = struct
     Logs.debug (fun k -> k "par-map: stop pool");
     P.stop ();
     res
+
+  (* Map on the list [l] with each call to [f] being associated one of the
+     resources from [resources] that is guaranteed not to be used concurrently
+     by another call to [f]. *)
+  let map_with_resource ~resources f l =
+    match l with
+    | [] -> []
+    | _ ->
+      if CCList.is_empty resources then
+        invalid_arg "map_with_resource: ~resources";
+      die_on_sigterm ();
+      let jobs = List.length resources in
+      let queue = CCBlockingQueue.create jobs in
+      List.iter (CCBlockingQueue.push queue) resources;
+      let f x =
+        let resource = CCBlockingQueue.take queue in
+        Fun.protect
+          ~finally:(fun () -> CCBlockingQueue.push queue resource)
+          (fun () -> f resource x)
+      in
+      Logs.debug (fun m -> m "par-map: create pool j=%d" jobs);
+      let module P = CCPool.Make (struct
+        let max_size = jobs
+      end) in
+      let res = P.Fut.map_l (P.Fut.make1 f) l |> P.Fut.get in
+      Logs.debug (fun m -> m "par-map: stop pool");
+      P.stop ();
+      res
 end
 
 module Git = struct
@@ -449,3 +477,13 @@ let start_server n server_fun sock =
 let establish_server n server_fun sockaddr =
   let sock, _ = mk_socket sockaddr in
   start_server n server_fun sock
+
+let with_affinity cpu f =
+  let aff = Processor.Affinity.get_ids () in
+  Processor.Affinity.set_ids [ cpu ];
+  Fun.protect ~finally:(fun () -> Processor.Affinity.set_ids aff) f
+
+let with_affinity_opt cpu f =
+  match cpu with
+  | None -> f ()
+  | Some cpu -> with_affinity cpu f
diff --git a/src/core/dune b/src/core/dune
index b2f3687..a7bb8c5 100644
--- a/src/core/dune
+++ b/src/core/dune
@@ -7,7 +7,7 @@
  (wrapped true)
  (libraries containers containers.unix containers-thread re re.perl csv iter
    printbox printbox-text logs logs.cli gnuplot ptime ptime.clock.os uuidm
-   sqlite3 sqlite3_utils cmdliner pp_loc)
+   sqlite3 sqlite3_utils cmdliner pp_loc processor)
  (flags :standard -w -5 -warn-error -a+8 -strict-sequence))
 
 (rule