--- a/src/sage/rings/function_field/function_field.py
+++ b/src/sage/rings/function_field/function_field.py
@@ -111,22 +111,21 @@ Function fields over the algebraic field are supported::
     sage: m = L.completion(pl, prec=5)
     sage: m(x)
     I + s + O(s^5)
-    sage: m(y)
+    sage: m(y)                             # long time (4s)
     -2*s + (-4 - I)*s^2 + (-15 - 4*I)*s^3 + (-75 - 23*I)*s^4 + (-413 - 154*I)*s^5 + O(s^6)
-    sage: m(y)^2 + m(y) + m(x) + 1/m(x)
+    sage: m(y)^2 + m(y) + m(x) + 1/m(x)    # long time (8s)
     O(s^5)
 
 TESTS::
 
     sage: TestSuite(J).run()
-    sage: TestSuite(K).run(max_runs=1024) # long time (5s)
-    sage: TestSuite(L).run(max_runs=64)   # long time (10s)
-    sage: TestSuite(M).run(max_runs=32)   # long time (30s)
-    sage: TestSuite(N).run(max_runs=64, skip = '_test_derivation')  # long time (8s)
-    sage: TestSuite(O).run(max_runs=128, skip = '_test_derivation') # long time (8s)
-
+    sage: TestSuite(K).run(max_runs=256)   # long time (10s)
+    sage: TestSuite(L).run(max_runs=8)     # long time (25s)
+    sage: TestSuite(M).run(max_runs=8)     # long time (35s)
+    sage: TestSuite(N).run(max_runs=8, skip = '_test_derivation')    # long time (15s)
+    sage: TestSuite(O).run()
     sage: TestSuite(R).run()
-    sage: TestSuite(S).run() # long time (3s)
+    sage: TestSuite(S).run()               # long time (4s)
 
 Global function fields
 ----------------------
@@ -287,7 +286,7 @@ class FunctionField(Field):
         TESTS::
 
             sage: K.<x> = FunctionField(QQ)
-            sage: TestSuite(K).run()
+            sage: TestSuite(K).run()               # long time (3s)
         """
         Field.__init__(self, base_field, names=names, category=category)
 
@@ -729,7 +728,7 @@ class FunctionField(Field):
         EXAMPLES::
 
             sage: K.<x> = FunctionField(QQ)
-            sage: TestSuite(K).run() # indirect doctest
+            sage: TestSuite(K).run()    # indirect doctest, long time (3s)
         """
         tester = self._tester(**options)
         S = tester.some_elements()
@@ -1209,7 +1208,7 @@ class FunctionField_polymod(FunctionField):
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L = K.extension(y^5 - x^3 - 3*x + x*y); L
             Function field in y defined by y^5 + x*y - x^3 - 3*x
-            sage: TestSuite(L).run()  # long time
+            sage: TestSuite(L).run(max_runs=512)   # long time (15s)
 
         We can set the variable name, which doesn't have to be y::
 
@@ -2888,7 +2887,8 @@ class FunctionField_simple(FunctionField_polymod):
             sage: F.<y> = K.extension(Y^3 - x^2*(x^2 + x + 1)^2)
             sage: O = K.maximal_order()
             sage: pls = [O.ideal(x-QQbar(sqrt(c))).place() for c in [-2, -1, 0, 1, 2]]
-            sage: all(q.place_below() == p for p in pls for q in F.places_above(p))
+            sage: all(q.place_below() == p         # long time (4s)
+            ....:     for p in pls for q in F.places_above(p))
             True
         """
         R = self.base_field()
@@ -3091,7 +3091,7 @@ class FunctionField_global(FunctionField_simple):
 
         sage: K.<x> = FunctionField(GF(4)); _.<Y> = K[]
         sage: L.<y> = K.extension((1 - x)*Y^7 - x^3)
-        sage: L.gaps()
+        sage: L.gaps()                         # long time (6s)
         [1, 2, 3]
 
     or may define a trivial extension::
@@ -3111,7 +3111,7 @@ class FunctionField_global(FunctionField_simple):
 
             sage: K.<x> = FunctionField(GF(5)); _.<Y> = K[]
             sage: L.<y> = K.extension(Y^3 - (x^3 - 1)/(x^3 - 2))
-            sage: TestSuite(L).run()
+            sage: TestSuite(L).run()               # long time (7s)
         """
         FunctionField_polymod.__init__(self, polynomial, names)
 
@@ -3807,7 +3807,7 @@ class RationalFunctionField(FunctionField):
 
             sage: K.<t> = FunctionField(CC); K
             Rational function field in t over Complex Field with 53 bits of precision
-            sage: TestSuite(K).run()
+            sage: TestSuite(K).run()               # long time (5s)
 
             sage: FunctionField(QQ[I], 'alpha')
             Rational function field in alpha over Number Field in I with defining polynomial x^2 + 1 with I = 1*I