diff --git a/acb_mat/mul.c b/acb_mat/mul.c
index a421f671..7d24aeab 100644
--- a/acb_mat/mul.c
+++ b/acb_mat/mul.c
@@ -68,7 +68,7 @@ acb_mat_mul(acb_mat_t C, const acb_mat_t A, const acb_mat_t B, slong prec)
     n = FLINT_MIN(ar, ac);
     n = FLINT_MIN(ac, bc);
 
-    if (n >= 5)
+    if (n >= 20)
     {
         abits = acb_mat_bits(A);
         bbits = acb_mat_bits(B);
diff --git a/acb_mat/solve_tril.c b/acb_mat/solve_tril.c
index 2e484507..6e2a2a97 100644
--- a/acb_mat/solve_tril.c
+++ b/acb_mat/solve_tril.c
@@ -99,7 +99,7 @@ void
 acb_mat_solve_tril(acb_mat_t X, const acb_mat_t L,
                                     const acb_mat_t B, int unit, slong prec)
 {
-    if (B->r < 8 || B->c < 8)
+    if (B->r < 40 || B->c < 40)
         acb_mat_solve_tril_classical(X, L, B, unit, prec);
     else
         acb_mat_solve_tril_recursive(X, L, B, unit, prec);
diff --git a/acb_mat/solve_triu.c b/acb_mat/solve_triu.c
index 6b846aa0..0f5a6278 100644
--- a/acb_mat/solve_triu.c
+++ b/acb_mat/solve_triu.c
@@ -99,7 +99,7 @@ void
 acb_mat_solve_triu(acb_mat_t X, const acb_mat_t U,
                                     const acb_mat_t B, int unit, slong prec)
 {
-    if (B->r < 8 || B->c < 8)
+    if (B->r < 40 || B->c < 40)
         acb_mat_solve_triu_classical(X, U, B, unit, prec);
     else
         acb_mat_solve_triu_recursive(X, U, B, unit, prec);
diff --git a/arb_mat/mul.c b/arb_mat/mul.c
index 2813528b..d67772f4 100644
--- a/arb_mat/mul.c
+++ b/arb_mat/mul.c
@@ -14,12 +14,18 @@
 void
 arb_mat_mul(arb_mat_t C, const arb_mat_t A, const arb_mat_t B, slong prec)
 {
-    if (arb_mat_nrows(A) >= 8 && arb_mat_ncols(A) >= 8 &&
-        arb_mat_ncols(B) >= 8)
-    {
-        arb_mat_mul_block(C, A, B, prec);
-    }
+    slong cutoff;
+
+    /* todo: detect small-integer matrices */
+    if (prec <= 2 * FLINT_BITS)
+        cutoff = 60;
+    else if (prec <= 8 * FLINT_BITS)
+        cutoff = 50;
     else
+        cutoff = 40;
+
+    if (arb_mat_nrows(A) <= cutoff || arb_mat_ncols(A) <= cutoff ||
+        arb_mat_ncols(B) <= cutoff)
     {
         if (flint_get_num_threads() > 1 &&
             ((double) arb_mat_nrows(A) *
@@ -34,5 +40,8 @@ arb_mat_mul(arb_mat_t C, const arb_mat_t A, const arb_mat_t B, slong prec)
             arb_mat_mul_classical(C, A, B, prec);
         }
     }
+    else
+    {
+        arb_mat_mul_block(C, A, B, prec);
+    }
 }
-
diff --git a/arb_mat/solve_tril.c b/arb_mat/solve_tril.c
index a2fad9d7..ec57eba6 100644
--- a/arb_mat/solve_tril.c
+++ b/arb_mat/solve_tril.c
@@ -99,7 +99,7 @@ void
 arb_mat_solve_tril(arb_mat_t X, const arb_mat_t L,
                                     const arb_mat_t B, int unit, slong prec)
 {
-    if (B->r < 8 || B->c < 8)
+    if (B->r < 40 || B->c < 40)
         arb_mat_solve_tril_classical(X, L, B, unit, prec);
     else
         arb_mat_solve_tril_recursive(X, L, B, unit, prec);
diff --git a/arb_mat/solve_triu.c b/arb_mat/solve_triu.c
index 956b5b19..d0315402 100644
--- a/arb_mat/solve_triu.c
+++ b/arb_mat/solve_triu.c
@@ -99,7 +99,7 @@ void
 arb_mat_solve_triu(arb_mat_t X, const arb_mat_t U,
                                     const arb_mat_t B, int unit, slong prec)
 {
-    if (B->r < 8 || B->c < 8)
+    if (B->r < 40 || B->c < 40)
         arb_mat_solve_triu_classical(X, U, B, unit, prec);
     else
         arb_mat_solve_triu_recursive(X, U, B, unit, prec);