diff --git a/rosette/solver/smt/enc-lit.rkt b/rosette/solver/smt/enc-lit.rkt
new file mode 100644
index 00000000..fa444c58
--- /dev/null
+++ b/rosette/solver/smt/enc-lit.rkt
@@ -0,0 +1,35 @@
+#lang racket/base
+
+(provide current-literal-encoder
+         enc-real
+         enc-integer)
+
+(require racket/match
+         racket/format
+         (prefix-in $ "smtlib2.rkt")
+         (only-in "../../base/core/bitvector.rkt"
+                  bitvector? bv bitvector-size
+                  @bveq @bvslt @bvsle @bvult @bvule
+                  @bvnot @bvor @bvand @bvxor @bvshl @bvlshr @bvashr
+                  @bvneg @bvadd @bvmul @bvudiv @bvsdiv @bvurem @bvsrem @bvsmod
+                  @concat @extract @zero-extend @sign-extend
+                  @integer->bitvector @bitvector->integer @bitvector->natural))
+
+(define (default-literal-encoder v)
+  (match v
+    [#t $true]
+    [#f $false]
+    [(? integer?) (enc-integer v)]
+    [(? real?) (enc-real v)]
+    [(bv lit t) ($bv lit (bitvector-size t))]
+    [_ (error 'enc "expected a boolean?, integer?, real?, or bitvector?, given ~a" v)]))
+
+(define current-literal-encoder
+  (make-parameter default-literal-encoder))
+
+(define-syntax-rule (enc-real v)
+  (if (exact? v) ($/ (numerator v) (denominator v)) (string->symbol (~r v))))
+
+(define-syntax-rule (enc-integer v)
+  (let ([v* (inexact->exact v)])
+    (if (< v* 0) ($- (abs v*)) v*)))
diff --git a/rosette/solver/smt/enc.rkt b/rosette/solver/smt/enc.rkt
index 7fe55c12..bdcf72cd 100644
--- a/rosette/solver/smt/enc.rkt
+++ b/rosette/solver/smt/enc.rkt
@@ -1,7 +1,8 @@
 #lang racket
 
-(require "env.rkt" 
-         (prefix-in $ "smtlib2.rkt") 
+(require "env.rkt"
+         "enc-lit.rkt"
+         (prefix-in $ "smtlib2.rkt")
          (only-in "../../base/core/term.rkt" expression expression? constant? term? get-type @app)
          (only-in "../../base/core/polymorphic.rkt" ite ite* =? guarded-test guarded-value)
          (only-in "../../base/core/distinct.rkt" @distinct?)
@@ -74,19 +75,7 @@
     [_ (error 'enc "cannot encode ~a to SMT" v)]))
 
 (define (enc-lit v env quantified)
-  (match v 
-    [#t $true]
-    [#f $false]
-    [(? integer?) (enc-integer v)]
-    [(? real?) (enc-real v)]
-    [(bv lit t) ($bv lit (bitvector-size t))]
-    [_ (error 'enc "expected a boolean?, integer?, real?, or bitvector?, given ~a" v)]))
-
-(define-syntax-rule (enc-real v)
-  (if (exact? v) ($/ (numerator v) (denominator v)) (string->symbol (~r v))))
-(define-syntax-rule (enc-integer v)
-  (let ([v* (inexact->exact v)])
-    (if (< v* 0) ($- (abs v*)) v*)))
+  ((current-literal-encoder) v))
 
 (define-syntax define-encoder
   (syntax-rules ()
diff --git a/test/base/real.rkt b/test/base/real.rkt
index 6df534e9..51837f2d 100644
--- a/test/base/real.rkt
+++ b/test/base/real.rkt
@@ -1,6 +1,7 @@
 #lang racket
 
-(require rackunit rackunit/text-ui  "common.rkt" "solver.rkt" 
+(require rackunit rackunit/text-ui  "common.rkt" "solver.rkt"
+         rosette/solver/smt/enc-lit
          rosette/solver/smt/z3
          rosette/solver/solution 
          rosette/lib/roseunit 
@@ -256,7 +257,19 @@
   (parameterize ([solver (z3  #:options (hash ':pp.decimal 'true ':pp.decimal-precision 15))])
     (check-= (abs ((solve (@= (@* xr xr) 2)) xr)) (abs (sqrt 2)) 1e-15)
     (solver-shutdown (solver))))
-  
+
+(define (check-qf-nra)
+  (parameterize ([solver (z3 #:logic 'QF_NRA)]
+                 [current-literal-encoder
+                  (let ([encode (current-literal-encoder)])
+                    (λ (x)
+                      (cond
+                        [(real? x) (enc-real x)]
+                        [else (encode x)])))])
+    (define-symbolic x @real?)
+    (check-pred sat? (solve (@= -2.0 x)))
+    (solver-shutdown (solver))))
+
 (define (check-division-simplifications div x y z [epsilon 0])
   (check-valid? (div 0 x) 0)
   (check-valid? (div x 1) x)
@@ -563,6 +576,7 @@
    (check-*-simplifications xr yr zr)
    (check-*-real-simplifications)
    (check-irrationals)
+   (check-qf-nra)
    (check-semantics @* xi yi zi)
    (check-semantics @* xr yr zr)))