diff --git a/qd-fun.lisp b/qd-fun.lisp
index 9564dccc374d5f34387f117431ae913fac4420ae..207a51b93e758228226214609f0da54851ceeee3 100644
--- a/qd-fun.lisp
+++ b/qd-fun.lisp
@@ -1188,7 +1188,10 @@ is the cosine of A"
      ;; atan(x) = pi/2-atan(1/x), for x > 1
      (sub-qd +qd-pi/2+
 	     (atan-qd/taylor (div-qd +qd-one+ y))))
+    ((qd-<= y (aref octi::+qd-atan-partition+ 0))
+     (atan-taylor y))
     (t
+     ;; The general case where the table is needed.
      (let* ((i (find-atan-partition y))
 	    (atan-xi (mul-qd +qd-pi/2+
 			     (rational-to-qd (/ (1- (+ i 2))
@@ -1244,6 +1247,8 @@ is the cosine of A"
 	  (neg-qd +qd-pi/4+))))
 
   (let ((arg (atan-qd/taylor (div-qd y (abs-qd x)))))
+    ;; arg = atan2(y,|x|), so |arg| <= pi/2.  Handle the case when x
+    ;; is negative.
     (cond ((minusp-qd x)
 	   (if (minusp-qd y)
 	       (- (neg-qd +qd-pi+) arg)
@@ -1254,12 +1259,12 @@ is the cosine of A"
 (defun atan2-qd (y x)
   "atan2(y, x) = atan(y/x), but carefully handling the quadrant"
   (declare (type %quad-double y x))
-  (atan2-qd/newton y x))
+  (atan2-qd/taylor y x))
 
 (defun atan-qd (y)
   "Return the arc tangent of the %QUAD-DOUBLE number Y"
   (declare (type %quad-double y))
-  (atan-qd/newton y))
+  (atan-qd/taylor y))
 
 (defun asin-qd (a)
   "Return the arc sine of the %QUAD-DOUBLE number A"
diff --git a/rt-tests.lisp b/rt-tests.lisp
index 69f6ee7c7bb54b34dae794a14ab117353c65c859..289131e246b1e9e110892d23fffef5d71887a2c4 100644
--- a/rt-tests.lisp
+++ b/rt-tests.lisp
@@ -222,6 +222,9 @@
   nil)
 
 (rt:deftest oct.atan.4
+    ;; We know atan(10^100) is pi/2 because atan(10^100) =
+    ;; pi/2-atan(10^-100) and atan(10^-100) is approx 10^-100, which
+    ;; is too small to affect pi/2.
     (let* ((arg #q1q100)
 	   (y (/ (atan arg) +pi+))
 	   (true #q.5))