diff -ru src/src/basemath/alglin1.c b/src/basemath/alglin1.c
--- src/src/basemath/alglin1.c	2012-09-25 23:10:46.000000000 +0200
+++ b/src/basemath/alglin1.c	2013-01-03 13:56:55.487513420 +0100
@@ -2969,6 +2969,21 @@
   return NULL; /* not reached */
 }
 
+/* A a 2x2 matrix
+   returns the determinant of A computed by the simple formula
+*/
+static GEN
+det2x2(GEN A)
+{
+  pari_sp av = avma;
+  GEN a = gcoeff(A, 1, 1),
+      b = gcoeff(A, 1, 2),
+      c = gcoeff(A, 2, 1),
+      d = gcoeff(A, 2, 2);
+  return gerepileupto(av, gsub(gmul(a, d), gmul(b, c)));
+}
+
+
 static GEN
 det_simple_gauss(GEN a, GEN data, pivot_fun pivot)
 {
@@ -3021,6 +3036,7 @@
   if (typ(a)!=t_MAT) pari_err(mattype1,"det2");
   if (!nbco) return gen_1;
   if (nbco != lg(a[1])-1) pari_err(mattype1,"det2");
+  if (nbco == 2) return det2x2 (a);
   pivot = get_pivot_fun(a, &data);
   return det_simple_gauss(a, data, pivot);
 }
@@ -3158,11 +3174,7 @@
   {
     case 0: return gen_1;
     case 1: return gcopy(gcoeff(M,1,1));
-    case 2: {
-      GEN a = gcoeff(M,1,1), b = gcoeff(M,1,2);
-      GEN c = gcoeff(M,2,1), d = gcoeff(M,2,2);
-      return gerepileupto(av, gsub(gmul(a,d), gmul(b,c)));
-    }
+    case 2: return det2x2(M);
   }
   if (max > ((n+2)>>1)) max = (n+2)>>1;
   for (j = 1; j <= n; j++)
@@ -3193,9 +3205,10 @@
   }
   if (best_row)
   {
+    double d = lbest-1;
     GEN s = NULL;
     long k;
-    bound /= (lbest-1);
+    bound /= d*d*d;
     for (k = 1; k < lbest; k++)
     {
       GEN c = coeff_det(M, best_row, best[k], max, bound);
@@ -3205,9 +3218,10 @@
   }
   if (best_col)
   {
+    double d = lbest-1;
     GEN s = NULL;
     long k;
-    bound /= (lbest-1);
+    bound /= d*d*d;
     for (k = 1; k < lbest; k++)
     {
       GEN c = coeff_det(M, best[k], best_col, max, bound);
@@ -3230,15 +3244,24 @@
   if (!n) return gen_1;
   if (n != lg(a[1])-1) pari_err(mattype1,"det");
   if (n == 1) return gcopy(gcoeff(a,1,1));
-  if (RgM_is_FpM(a, &p) && p)
+  if (RgM_is_FpM(a, &p))
   {
-    pari_sp av = avma;
-    return gerepilecopy(av, Fp_to_mod(FpM_det(RgM_to_FpM(a, p), p), p));
+    pari_sp av;
+    if (!p)
+    { /* ZM */
+      return det_simple_gauss(a, NULL, &gauss_get_pivot_NZ);
+    }
+    else
+    { /* FpM */
+      av = avma;
+      return gerepilecopy(av, Fp_to_mod(FpM_det(RgM_to_FpM(a, p), p), p));
+    }
   }
+  if (n == 2) return det2x2 (a);
   pivot = get_pivot_fun(a, &data);
   if (pivot != gauss_get_pivot_NZ) return det_simple_gauss(a, data, pivot);
-  B = (double)n; B = B*B; B = B*B;
-  return det_develop(a, 7, B);
+  B = (double)n;
+  return det_develop(a, 7, B*B*B);
 }