diff --git a/libguile/instructions.c b/libguile/instructions.c
index a38035d25..3d20a6be8 100644
--- a/libguile/instructions.c
+++ b/libguile/instructions.c
@@ -40,6 +40,7 @@ SCM_SYMBOL (sym_bang, "!");
     M(X8_S8_I16)                                \
     M(X8_S12_S12)                               \
     M(X8_S12_C12)                               \
+    M(X8_S12_Z12)                               \
     M(X8_C12_C12)                               \
     M(X8_F12_F12)                               \
     M(X8_S8_S8_S8)                              \
diff --git a/libguile/vm-engine.c b/libguile/vm-engine.c
index a70f78a1c..e07bf46e5 100644
--- a/libguile/vm-engine.c
+++ b/libguile/vm-engine.c
@@ -4100,11 +4100,77 @@ VM_NAME (scm_i_thread *thread, struct scm_vm *vp,
       NEXT (1);
     }
 
-  VM_DEFINE_OP (218, unused_218, NULL, NOP)
-  VM_DEFINE_OP (219, unused_219, NULL, NOP)
-  VM_DEFINE_OP (220, unused_220, NULL, NOP)
-  VM_DEFINE_OP (221, unused_221, NULL, NOP)
-  VM_DEFINE_OP (222, unused_222, NULL, NOP)
+  VM_DEFINE_OP (218, s64_imm_numerically_equal, "s64-imm=?", OP1 (X8_S12_Z12))
+    {
+      scm_t_uint16 a;
+      scm_t_int64 x, y;
+
+      a = (op >> 8) & 0xfff;
+      x = SP_REF_S64 (a);
+
+      y = ((scm_t_int32) op) >> 20; /* Sign extension.  */
+
+      vp->compare_result = x == y ? SCM_F_COMPARE_EQUAL : SCM_F_COMPARE_NONE;
+
+      NEXT (1);
+    }
+
+  VM_DEFINE_OP (219, u64_imm_less, "u64-imm<?", OP1 (X8_S12_C12))
+    {
+      scm_t_uint16 a;
+      scm_t_uint64 x, y;
+
+      UNPACK_12_12 (op, a, y);
+      x = SP_REF_U64 (a);
+
+      vp->compare_result = x < y ? SCM_F_COMPARE_LESS_THAN : SCM_F_COMPARE_NONE;
+
+      NEXT (1);
+    }
+
+  VM_DEFINE_OP (220, imm_u64_less, "imm-u64<?", OP1 (X8_S12_C12))
+    {
+      scm_t_uint16 a;
+      scm_t_uint64 x, y;
+
+      UNPACK_12_12 (op, a, x);
+      y = SP_REF_U64 (a);
+
+      vp->compare_result = x < y ? SCM_F_COMPARE_LESS_THAN : SCM_F_COMPARE_NONE;
+
+      NEXT (1);
+    }
+
+  VM_DEFINE_OP (221, s64_imm_less, "s64-imm<?", OP1 (X8_S12_Z12))
+    {
+      scm_t_uint16 a;
+      scm_t_int64 x, y;
+
+      a = (op >> 8) & 0xfff;
+      x = SP_REF_S64 (a);
+
+      y = ((scm_t_int32) op) >> 20; /* Sign extension.  */
+
+      vp->compare_result = x < y ? SCM_F_COMPARE_LESS_THAN : SCM_F_COMPARE_NONE;
+
+      NEXT (1);
+    }
+
+  VM_DEFINE_OP (222, imm_s64_less, "imm-s64<?", OP1 (X8_S12_Z12))
+    {
+      scm_t_uint16 a;
+      scm_t_int64 x, y;
+
+      a = (op >> 8) & 0xfff;
+      y = SP_REF_S64 (a);
+
+      x = ((scm_t_int32) op) >> 20; /* Sign extension.  */
+
+      vp->compare_result = x < y ? SCM_F_COMPARE_LESS_THAN : SCM_F_COMPARE_NONE;
+
+      NEXT (1);
+    }
+
   VM_DEFINE_OP (223, unused_223, NULL, NOP)
   VM_DEFINE_OP (224, unused_224, NULL, NOP)
   VM_DEFINE_OP (225, unused_225, NULL, NOP)
diff --git a/module/language/bytecode.scm b/module/language/bytecode.scm
index 8372feb02..b6be04178 100644
--- a/module/language/bytecode.scm
+++ b/module/language/bytecode.scm
@@ -42,6 +42,7 @@
       ((X8_S8_I16) 2)
       ((X8_S12_S12) 2)
       ((X8_S12_C12) 2)
+      ((X8_S12_Z12) 2)
       ((X8_C12_C12) 2)
       ((X8_F12_F12) 2)
       ((X8_S8_S8_S8) 3)
diff --git a/module/language/cps/compile-bytecode.scm b/module/language/cps/compile-bytecode.scm
index 429f7e777..f11a4c1ad 100644
--- a/module/language/cps/compile-bytecode.scm
+++ b/module/language/cps/compile-bytecode.scm
@@ -425,6 +425,12 @@
         (binary op emit-je emit-jne a b))
       (define (binary-< emit-<? a b)
         (binary emit-<? emit-jl emit-jnl a b))
+      (define (binary-test/imm op a b)
+        (op asm (from-sp (slot a)) b)
+        (emit-branch emit-je emit-jne))
+      (define (binary-</imm op a b)
+        (op asm (from-sp (slot a)) b)
+        (emit-branch emit-jl emit-jnl))
       (match exp
         (($ $primcall 'heap-object? #f (a)) (unary emit-heap-object? a))
         (($ $primcall 'null? #f (a)) (unary emit-null? a))
@@ -451,9 +457,15 @@
         (($ $primcall '< #f (a b)) (binary-< emit-<? a b))
         (($ $primcall '= #f (a b)) (binary-test emit-=? a b))
         (($ $primcall 'u64-< #f (a b)) (binary-< emit-u64<? a b))
+        (($ $primcall 'u64-imm-< b (a)) (binary-</imm emit-u64-imm<? a b))
+        (($ $primcall 'imm-u64-< b (a)) (binary-</imm emit-imm-u64<? a b))
         (($ $primcall 'u64-= #f (a b)) (binary-test emit-u64=? a b))
+        (($ $primcall 'u64-imm-= b (a)) (binary-test/imm emit-s64-imm=? a b))
+        (($ $primcall 's64-= #f (a b)) (binary-test emit-u64=? a b))
+        (($ $primcall 's64-imm-= b (a)) (binary-test/imm emit-s64-imm=? a b))
         (($ $primcall 's64-< #f (a b)) (binary-< emit-s64<? a b))
-        (($ $primcall 's64-= #f (a b)) (binary-test emit-s64=? a b))
+        (($ $primcall 's64-imm-< b (a)) (binary-</imm emit-s64-imm<? a b))
+        (($ $primcall 'imm-s64-< b (a)) (binary-</imm emit-imm-s64<? a b))
         (($ $primcall 'f64-< #f (a b)) (binary-< emit-f64<? a b))
         (($ $primcall 'f64-= #f (a b)) (binary-test emit-f64=? a b))))
 
diff --git a/module/language/cps/effects-analysis.scm b/module/language/cps/effects-analysis.scm
index dd24e7398..178079e79 100644
--- a/module/language/cps/effects-analysis.scm
+++ b/module/language/cps/effects-analysis.scm
@@ -424,9 +424,15 @@ is or might be a read or a write to the same location as A."
   ((= . _)                         &type-check)
   ((< . _)                         &type-check)
   ((u64-= . _))
+  ((u64-imm-= . _))
   ((u64-< . _))
+  ((u64-imm-< . _))
+  ((imm-u64-< . _))
   ((s64-= . _))
+  ((s64-imm-= . _))
   ((s64-< . _))
+  ((s64-imm-< . _))
+  ((imm-s64-< . _))
   ((f64-= . _))
   ((f64-< . _))
   ((zero? . _)                     &type-check)
diff --git a/module/language/cps/primitives.scm b/module/language/cps/primitives.scm
index ed1492fc3..ed2aeaedf 100644
--- a/module/language/cps/primitives.scm
+++ b/module/language/cps/primitives.scm
@@ -139,7 +139,6 @@ before it is lowered to CPS?"
     u64-=
 
     s64-<
-    s64-=
 
     f64-<
     f64-=))
diff --git a/module/language/cps/reify-primitives.scm b/module/language/cps/reify-primitives.scm
index 1c5b31949..680c1b771 100644
--- a/module/language/cps/reify-primitives.scm
+++ b/module/language/cps/reify-primitives.scm
@@ -153,12 +153,13 @@
                        ($continue kb src ($const b))))))
       (($ $kargs names vars ($ $continue k src ($ $primcall name param args)))
        (cond
-        ((or (prim-instruction name) (branching-primitive? name))
+        ((prim-instruction name)
          ;; Assume arities are correct.
          (let ()
            (define (u6? val) (and (exact-integer? val) (<= 0 val 63)))
            (define (u8? val) (and (exact-integer? val) (<= 0 val 255)))
-           (define-syntax-rule (reify-constants wrap
+           (define-syntax-rule (reify-constants
+                                wrap
                                 ((op (pred? c) in ...) (op* out ...))
                                 ...
                                 (_ default))
@@ -211,6 +212,42 @@
                                ($continue k src ($call proc args))))
            (let$ body (resolve-prim name kproc src))
            (setk label ($kargs names vars ,body))))))
+      (($ $kargs names vars
+          ($ $continue kf src ($ $branch kt ($ $primcall name param args))))
+       (let ()
+         (define (u11? val) (<= 0 val #x7ff))
+         (define (u12? val) (<= 0 val #xfff))
+         (define (s12? val) (<= (- #x800) val #x7ff))
+         (define-syntax-rule (reify-constants ((op (pred? c) in ...)
+                                               wrap-op (op* out ...))
+                                              ...
+                                              (_ default))
+           (match name
+             ('op
+              (if (pred? param)
+                  cps
+                  (match args
+                    ((in ...)
+                     (with-cps cps
+                       (letv c)
+                       (letk kconst
+                             ($kargs ('c) (c)
+                               ($continue kf src
+                                 ($branch kt ($primcall 'op* #f (out ...))))))
+                       (setk label
+                             ($kargs names vars
+                               ($continue kconst src
+                                 ($primcall 'wrap-op param ())))))))))
+             ...
+             (_ default)))
+         (reify-constants
+          ((u64-imm-= (u11? b) a) load-u64 (u64-= a b))
+          ((u64-imm-< (u12? b) a) load-u64 (u64-< a b))
+          ((imm-u64-< (u12? a) b) load-u64 (u64-< a b))
+          ((s64-imm-= (s12? b) a) load-s64 (s64-= a b))
+          ((s64-imm-< (s12? b) a) load-s64 (s64-< a b))
+          ((imm-s64-< (s12? a) b) load-s64 (s64-< a b))
+          (_ cps))))
       (($ $kargs names vars ($ $continue k src ($ $call proc args)))
        (with-cps cps
          (let$ k (uniquify-receive k))
diff --git a/module/language/cps/specialize-numbers.scm b/module/language/cps/specialize-numbers.scm
index 37a17057c..ced7a3b3b 100644
--- a/module/language/cps/specialize-numbers.scm
+++ b/module/language/cps/specialize-numbers.scm
@@ -203,7 +203,7 @@
         ($primcall unbox-a #f (scm))))))
 
 (define (specialize-fixnum-comparison cps kf kt src op a b)
-  (let ((op (symbol-append 's64- op)))
+  (let ((op (match op ('= 'u64-=) ('< 's64-<))))
     (with-cps cps
       (letv s64-a s64-b)
       (letk kop ($kargs ('s64-b) (s64-b)
@@ -217,7 +217,7 @@
           ($primcall 'untag-fixnum #f (a)))))))
 
 (define (specialize-fixnum-scm-comparison cps kf kt src op a-fx b-scm)
-  (let ((s64-op (match op ('= 's64-=) ('< 's64-<))))
+  (let ((s64-op (match op ('= 'u64-=) ('< 's64-<))))
     (with-cps cps
       (letv a b sunk)
       (letk kheap ($kargs ('sunk) (sunk)
diff --git a/module/language/cps/type-fold.scm b/module/language/cps/type-fold.scm
index 27b9dd827..4e8108fbb 100644
--- a/module/language/cps/type-fold.scm
+++ b/module/language/cps/type-fold.scm
@@ -51,9 +51,13 @@
 (define-syntax-rule (define-branch-folder-alias to from)
   (hashq-set! *branch-folders* 'to (hashq-ref *branch-folders* 'from)))
 
-(define-syntax-rule (define-unary-branch-folder (name arg min max) body ...)
+(define-syntax-rule (define-unary-branch-folder* (name param arg min max)
+                      body ...)
   (define-branch-folder name (lambda (param arg min max) body ...)))
 
+(define-syntax-rule (define-unary-branch-folder (name arg min max) body ...)
+  (define-unary-branch-folder* (name param arg min max) body ...))
+
 (define-syntax-rule (define-binary-branch-folder (name arg0 min0 max0
                                                        arg1 min1 max1)
                       body ...)
@@ -151,13 +155,33 @@
 ;;
 ;; (define-branch-folder-alias f64-< <)
 
+(define-unary-branch-folder* (u64-imm-= c type min max)
+  (cond
+   ((= c min max) (values #t #t))
+   ((<= min c max) (values #f #f))
+   (else (values #t #f))))
+(define-branch-folder-alias s64-imm-= u64-imm-=)
+
+(define-unary-branch-folder* (u64-imm-< c type min max)
+  (cond
+   ((< max c) (values #t #t))
+   ((>= min c) (values #t #f))
+   (else (values #f #f))))
+(define-branch-folder-alias s64-imm-< u64-imm-<)
+
+(define-unary-branch-folder* (imm-u64-< c type min max)
+  (cond
+   ((< c min) (values #t #t))
+   ((>= c max) (values #t #f))
+   (else (values #f #f))))
+(define-branch-folder-alias imm-s64-< imm-u64-<)
+
 (define-binary-branch-folder (= type0 min0 max0 type1 min1 max1)
   (case (compare-integer-ranges type0 min0 max0 type1 min1 max1)
     ((=) (values #t #t))
     ((< >) (values #t #f))
     (else (values #f #f))))
 (define-branch-folder-alias u64-= =)
-(define-branch-folder-alias s64-= =)
 
 
 
diff --git a/module/language/cps/types.scm b/module/language/cps/types.scm
index 7dcafd663..841d29f28 100644
--- a/module/language/cps/types.scm
+++ b/module/language/cps/types.scm
@@ -471,6 +471,12 @@ minimum, and maximum."
     (let ((true? (not (zero? succ))))
       body ...)))
 
+(define-syntax-rule (define-predicate-inferrer/param
+                      (name param arg ... true?) body ...)
+  (define-type-inferrer* (name param succ arg ...)
+    (let ((true? (not (zero? succ))))
+      body ...)))
+
 (define-syntax define-simple-type-checker
   (lambda (x)
     (define (parse-spec l)
@@ -1007,16 +1013,31 @@ minimum, and maximum."
 (define-simple-type-checker (< &real &real))
 (define-<-inferrer (< &real &exact-integer))
 
-(define-simple-type-checker (u64-= &u64 &u64))
 (define-=-inferrer (u64-= &u64))
-(define-simple-type-checker (u64-< &u64 &u64))
 (define-<-inferrer (u64-< &u64 &u64))
 
-(define-simple-type-checker (s64-= &s64 &s64))
-(define-=-inferrer (s64-= &s64))
-(define-simple-type-checker (s64-< &s64 &s64))
 (define-<-inferrer (s64-< &s64 &s64))
 
+(define-predicate-inferrer/param (u64-imm-= b a true?)
+  (when true?
+    (restrict! a (logior &u64 &s64) (max (&min a) b) (min (&max a) b))))
+
+(define-predicate-inferrer/param (u64-imm-< b a true?)
+  (if true?
+      (restrict! a (logior &u64 &s64) (&min a) (min (&max a) (1- b)))
+      (restrict! a (logior &u64 &s64) (max (&min a) b) (&max a))))
+
+(define-predicate-inferrer/param (imm-u64-< b a true?)
+  (if true?
+      (restrict! a (logior &u64 &s64) (max (1+ (&min a)) b) (&max a))
+      (restrict! a (logior &u64 &s64) (&min a) (min (&max a) b))))
+
+(define-type-aliases u64-imm-= s64-imm-=)
+(define-type-aliases u64-imm-< s64-imm-<)
+(define-type-aliases imm-u64-< imm-s64-<)
+
+
+
 ;; Unfortunately, we can't define f64 comparison inferrers because of
 ;; not-a-number values.
 
diff --git a/module/system/vm/assembler.scm b/module/system/vm/assembler.scm
index 718ff5ea2..3fd5bba79 100644
--- a/module/system/vm/assembler.scm
+++ b/module/system/vm/assembler.scm
@@ -66,8 +66,12 @@
 
             emit-u64=?
             emit-u64<?
-            emit-s64=?
+            emit-u64-imm<?
+            emit-imm-u64<?
+            emit-s64-imm=?
             emit-s64<?
+            emit-s64-imm<?
+            emit-imm-s64<?
             emit-f64=?
             emit-f64<?
             emit-=?
@@ -341,6 +345,12 @@
         (z (check-urange z #xfff)))
     (logior x (ash y 8) (ash z 20))))
 
+(define-inline (pack-u8-u12-s12 x y z)
+  (let ((x (check-urange x #xff))
+        (y (check-urange y #xfff))
+        (z (check-srange z #xfff)))
+    (logior x (ash y 8) (ash z 20))))
+
 (define-inline (pack-u8-u8-u16 x y z)
   (let ((x (check-urange x #xff))
         (y (check-urange y #xff))
@@ -617,6 +627,8 @@ later by the linker."
             (emit asm (pack-u8-u12-u12 opcode a b)))
            ((X8_S12_C12 a b)
             (emit asm (pack-u8-u12-u12 opcode a b)))
+           ((X8_S12_Z12 a b)
+            (emit asm (pack-u8-u12-s12 opcode a b)))
            ((X8_C12_C12 a b)
             (emit asm (pack-u8-u12-u12 opcode a b)))
            ((X8_F12_F12 a b)
@@ -803,6 +815,14 @@ later by the linker."
     (emit-push asm a)
     (encode-X8_S12_S12-X8_C24 asm 0 0 const opcode)
     (emit-pop asm dst))))
+(define (encode-X8_S12_C12!/shuffle asm a const opcode)
+  (cond
+   ((< a (ash 1 12))
+    (encode-X8_S12_C12 asm a const opcode))
+   (else
+    (emit-push asm a)
+    (encode-X8_S12_C12 asm 0 const opcode)
+    (emit-drop asm 1))))
 (define (encode-X8_S12_C12<-/shuffle asm dst const opcode)
   (cond
    ((< dst (ash 1 12))
@@ -812,6 +832,14 @@ later by the linker."
     (emit-push asm dst)
     (encode-X8_S12_C12 asm 0 const opcode)
     (emit-pop asm dst))))
+(define (encode-X8_S12_Z12!/shuffle asm a const opcode)
+  (cond
+   ((< a (ash 1 12))
+    (encode-X8_S12_Z12 asm a const opcode))
+   (else
+    (emit-push asm a)
+    (encode-X8_S12_Z12 asm 0 const opcode)
+    (emit-drop asm 1))))
 (define (encode-X8_S8_I16<-/shuffle asm dst imm opcode)
   (cond
    ((< dst (ash 1 8))
@@ -877,7 +905,9 @@ later by the linker."
       (('<- 'X8_S12_S12)         #'encode-X8_S12_S12<-/shuffle)
       (('! 'X8_S12_S12 'X8_C24)  #'encode-X8_S12_S12-X8_C24!/shuffle)
       (('<- 'X8_S12_S12 'X8_C24) #'encode-X8_S12_S12-X8_C24<-/shuffle)
+      (('! 'X8_S12_C12)          #'encode-X8_S12_C12!/shuffle)
       (('<- 'X8_S12_C12)         #'encode-X8_S12_C12<-/shuffle)
+      (('! 'X8_S12_Z12)          #'encode-X8_S12_Z12!/shuffle)
       (('<- 'X8_S8_I16)          #'encode-X8_S8_I16<-/shuffle)
       (('! 'X8_S8_S8_S8)         #'encode-X8_S8_S8_S8!/shuffle)
       (('<- 'X8_S8_S8_S8)        #'encode-X8_S8_S8_S8<-/shuffle)
@@ -919,6 +949,7 @@ later by the linker."
           ('X8_S8_I16 #'(a imm))
           ('X8_S12_S12 #'(a b))
           ('X8_S12_C12 #'(a b))
+          ('X8_S12_Z12 #'(a b))
           ('X8_C12_C12 #'(a b))
           ('X8_F12_F12 #'(a b))
           ('X8_S8_S8_S8 #'(a b c))
diff --git a/module/system/vm/disassembler.scm b/module/system/vm/disassembler.scm
index 89acf6090..cb6447901 100644
--- a/module/system/vm/disassembler.scm
+++ b/module/system/vm/disassembler.scm
@@ -72,6 +72,11 @@
       s
       (- s (ash 1 24))))
 
+(define (unpack-s12 s)
+  (if (zero? (logand s (ash 1 11)))
+      s
+      (- s (ash 1 12))))
+
 (define (unpack-s32 s)
   (if (zero? (logand s (ash 1 31)))
       s
@@ -97,6 +102,9 @@
             X8_F12_F12)
            #'((logand (ash word -8) #xfff)
               (ash word -20)))
+          ((X8_S12_Z12)
+           #'((logand (ash word -8) #xfff)
+              (unpack-s12 (ash word -20))))
           ((X8_S8_S8_S8
             X8_S8_S8_C8
             X8_S8_C8_S8)