diff --git a/doc/source/fq_default.rst b/doc/source/fq_default.rst
index f74f136e9b..467132b10c 100644
--- a/doc/source/fq_default.rst
+++ b/doc/source/fq_default.rst
@@ -104,10 +104,13 @@ Context Management
 
     Prints the context information to ``stdout``.
 
-.. function:: void fq_default_ctx_randtest(fq_default_ctx_t ctx)
+.. function:: void fq_default_ctx_init_randtest(fq_default_ctx_t ctx, flint_rand_t state, int type)
 
-    Initializes ``ctx`` to a random finite field.  Assumes that
-    ``fq_default_ctx_init`` has not been called on ``ctx`` already.
+    Initializes ``ctx`` to a random finite field where the prime and degree is
+    set according to ``type``.
+    Assumes that ``fq_default_ctx_init`` has not been called on ``ctx`` already.
+    To see what prime and degrees may be output, see
+    ``type`` in :func:`_nmod_poly_conway_rand`.
 
 .. function:: void fq_default_get_coeff_fmpz(fmpz_t c, fq_default_t op, slong n, const fq_default_ctx_t ctx)
 
diff --git a/src/fq_default.h b/src/fq_default.h
index 6406358f99..9d2e82d67e 100644
--- a/src/fq_default.h
+++ b/src/fq_default.h
@@ -229,6 +229,7 @@ int fq_default_ctx_fprint(FILE * file, const fq_default_ctx_t ctx);
 #endif
 
 void fq_default_ctx_print(const fq_default_ctx_t ctx);
+void fq_default_ctx_init_randtest(fq_default_ctx_t ctx, flint_rand_t state, int type);
 
 /* Memory management  *********************************************************/
 
diff --git a/src/fq_default/ctx.c b/src/fq_default/ctx.c
index 778bb3df15..0422367589 100644
--- a/src/fq_default/ctx.c
+++ b/src/fq_default/ctx.c
@@ -199,3 +199,22 @@ void fq_default_ctx_modulus(fmpz_mod_poly_t p, const fq_default_ctx_t ctx)
         fmpz_mod_poly_set(p, FQ_DEFAULT_CTX_FQ(ctx)->modulus, mod);
     }
 }
+
+/* FIXME: fq_ctx_init_randtest only tests nmod sized primes, so that's
+   all we'll do here too? */
+void fq_default_ctx_init_randtest(fq_default_ctx_t ctx, flint_rand_t state, int type)
+{
+    ulong prime;
+    slong degree;
+    fmpz_t p;
+
+    /* select a prime and degree to create the finite field */
+    prime = _nmod_poly_conway_rand(&degree, state, type);
+
+    /* fq_default initialisation wants an fmpz_t for the prime */
+    fmpz_init(p);
+    fmpz_set_ui(p, prime);
+
+    /* Initialise the context using the prime and degree selected above */
+    fq_default_ctx_init(ctx, p, degree, "x");
+}
diff --git a/src/fq_default/test/t-init.c b/src/fq_default/test/t-init.c
index ae29d4d802..af8ec96aa1 100644
--- a/src/fq_default/test/t-init.c
+++ b/src/fq_default/test/t-init.c
@@ -81,5 +81,21 @@ TEST_FUNCTION_START(fq_default_init, state)
         fmpz_clear(p);
     }
 
+    for (i = 0; i < 100 * flint_test_multiplier(); i++)
+    {
+        fq_default_ctx_t ctx;
+        fq_default_t fq;
+
+        /* Sets the type used internally for prime selection.
+           See _nmod_poly_conway_rand for more info. */
+        int type = n_randint(state, 4);
+
+        fq_default_ctx_init_randtest(ctx, state, type);
+        fq_default_init(fq, ctx);
+        fq_default_clear(fq, ctx);
+        fq_default_randtest(fq, state, ctx);
+        fq_default_ctx_clear(ctx);
+    }
+
     TEST_FUNCTION_END(state);
 }