diff --git a/Makefile b/Makefile
index bb27775..b19fe3e 100644
--- a/Makefile
+++ b/Makefile
@@ -20,11 +20,11 @@ BUILD_IBIN = build/obj/bin
 DOXYGEN ?= doxygen
 
 ifeq ($(UNAME),Darwin)
-CC = clang
-CXX = clang++
+CC ?= clang
+CXX ?= clang++
 else
-CC = gcc
-CXX = g++
+CC ?= gcc
+CXX ?= g++
 endif
 LD = $(CC)
 LDXX = $(CXX)
diff --git a/_aux/ristretto/ristretto.sage b/_aux/ristretto/ristretto.sage
index 4bb08cc..41b0d22 100644
--- a/_aux/ristretto/ristretto.sage
+++ b/_aux/ristretto/ristretto.sage
@@ -121,6 +121,8 @@ class QuotientEdwardsPoint(object):
         else:
             return self.__class__(-self.x, -self.y)
     
+    def doubleAndEncodeSpec(self):
+        return (self+self).encode()
 
     # Utility functions
     @classmethod
@@ -203,7 +205,42 @@ class RistrettoPoint(QuotientEdwardsPoint):
             if negative(isr^2*num*y*t): y = -y
             s = isr*y*(z-y)
             
-        
+        return self.gfToBytes(s,mustBePositive=True)
+      
+    @optimized_version_of("doubleAndEncodeSpec")
+    def doubleAndEncode(self):
+        X,Y,Z,T = self.xyzt()
+        a,d,mneg = self.a,self.d,self.mneg
+
+        if self.cofactor==8:
+            e = 2*X*Y
+            f = Z^2+d*T^2
+            g = Y^2-a*X^2
+            h = Z^2-d*T^2
+            
+            inv1 = inv0(e*f*g*h)
+            z_inv = inv1*e*g # 1 / (f*h)
+            t_inv = inv1*f*h
+        
+            if negative(e*g*z_inv):
+                if a==-1: sqrta = self.i
+                else:     sqrta = -1
+                e,f,g,h = g,h,-e,f*sqrta
+                factor = self.i
+            else:
+                factor = self.magic
+            
+            if negative(h*e*z_inv): g=-g
+            s = (h-g)*factor*g*t_inv
+            
+        else:
+            foo = Y^2+a*X^2
+            bar = X*Y
+            den = inv0(foo*bar)
+            if negative(2*bar^2*den): tmp = a*X^2
+            else: tmp = Y^2
+            s = self.magic*(Z^2-tmp)*foo*den
+            
         return self.gfToBytes(s,mustBePositive=True)
         
     @classmethod
@@ -466,6 +503,54 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
         x = 2*s / (1+a*s^2)
         y = (1-a*s^2) / t
         return cls(x,sgn*y)
+
+    @optimized_version_of("doubleAndEncodeSpec")
+    def doubleAndEncode(self):
+        X,Y,Z,T = self.xyzt()
+        a,d = self.a,self.d
+        
+        if self.cofactor == 8:
+            # Cofactor 8 version
+            # Simulate IMAGINE_TWIST because that's how libdecaf does it
+            X = self.i*X
+            T = self.i*T
+            a = -a
+            d = -d
+            # TODO: This is only being called for a=-1, so could
+            # be wrong for a=1
+            
+            e = 2*X*Y
+            f = Y^2+a*X^2
+            g = Y^2-a*X^2
+            h = Z^2-d*T^2
+            
+            eim = e*self.isoMagic
+            inv = inv0(eim*g*f*h)
+            fh_inv = eim*g*inv*self.i
+            
+            if negative(eim*g*fh_inv):
+                idf = g*self.isoMagic*self.i
+                bar = f
+                foo = g
+                test = eim*f
+            else:
+                idf = eim
+                bar = h
+                foo = -eim
+                test = g*h
+            
+            if negative(test*fh_inv): bar =- bar
+            s = idf*(foo+bar)*inv*f*h
+        
+        else:
+            xy = X*Y
+            h = Z^2-d*T^2
+            inv = inv0(xy*h)
+            if negative(inv*2*xy^2*self.isoMagic): tmp = Y
+            else: tmp = X
+            s = tmp^2*h*inv # = X/Y or Y/X, interestingly
+            
+        return self.gfToBytes(s,mustBePositive=True)
             
     @classmethod
     def elligatorSpec(cls,r0,fromR=False):
@@ -696,7 +781,6 @@ def test(cls,n):
         if Q1 + Q0 != Q2: raise TestFailedException("Scalarmul doesn't work")
         Q = Q1
         
-   
 def testElligator(cls,n):
     print "Testing elligator on %s" % cls.__name__
     for i in xrange(n):
@@ -716,9 +800,6 @@ def testElligator(cls,n):
                 #break
         else:
             pass # TODO
-        
-
-
 
 def gangtest(classes,n):
     print "Gang test",[cls.__name__ for cls in classes]
@@ -747,18 +828,37 @@ def gangtest(classes,n):
                 print c,binascii.hexlify(ret)
             print
 
-
-test(Ed25519Point,100)
-test(NegEd25519Point,100)
-test(IsoEd25519Point,100)
-test(IsoEd448Point,100)
-test(TwistedEd448GoldilocksPoint,100)
-test(Ed448GoldilocksPoint,100)
-testElligator(Ed25519Point,100)
-testElligator(NegEd25519Point,100)
-testElligator(IsoEd25519Point,100)
-testElligator(IsoEd448Point,100)
-testElligator(Ed448GoldilocksPoint,100)
-testElligator(TwistedEd448GoldilocksPoint,100)
-gangtest([IsoEd448Point,TwistedEd448GoldilocksPoint,Ed448GoldilocksPoint],100)
-gangtest([Ed25519Point,IsoEd25519Point],100)
+def testDoubleAndEncode(cls,n):
+    print "Testing doubleAndEncode on %s" % cls.__name__
+    
+    P = cls()
+    for i in xrange(cls.cofactor):
+        Q = P.torque()
+        assert P.doubleAndEncode() == Q.doubleAndEncode()
+        P = Q
+    
+    for i in xrange(n):
+        r1 = randombytes(cls.encLen)
+        r2 = randombytes(cls.encLen)
+        u = cls.elligator(r1) + cls.elligator(r2)
+        assert u.doubleAndEncode() == u.torque().doubleAndEncode()
+
+testDoubleAndEncode(Ed25519Point,100)
+testDoubleAndEncode(NegEd25519Point,100)
+testDoubleAndEncode(IsoEd25519Point,100)
+testDoubleAndEncode(IsoEd448Point,100)
+testDoubleAndEncode(TwistedEd448GoldilocksPoint,100)
+#test(Ed25519Point,100)
+#test(NegEd25519Point,100)
+#test(IsoEd25519Point,100)
+#test(IsoEd448Point,100)
+#test(TwistedEd448GoldilocksPoint,100)
+#test(Ed448GoldilocksPoint,100)
+#testElligator(Ed25519Point,100)
+#testElligator(NegEd25519Point,100)
+#testElligator(IsoEd25519Point,100)
+#testElligator(IsoEd448Point,100)
+#testElligator(Ed448GoldilocksPoint,100)
+#testElligator(TwistedEd448GoldilocksPoint,100)
+#gangtest([IsoEd448Point,TwistedEd448GoldilocksPoint,Ed448GoldilocksPoint],100)
+#gangtest([Ed25519Point,IsoEd25519Point],100)
diff --git a/src/generator/curve_data.py b/src/generator/curve_data.py
index 8e7e8d9..f1773be 100644
--- a/src/generator/curve_data.py
+++ b/src/generator/curve_data.py
@@ -133,8 +133,11 @@ for curve,data in curve_data.items():
         data["eddsa_sigma_iso"] = 0
         
     if "rist_base_decoded" not in data:
+        def xord(x):
+            if isinstance(x,str): return ord(x)
+            else: return x
         data["rist_base_decoded"] = sum(
-                ord(b)<<(8*i) for i,b in enumerate(unhexlify(data["rist_base"]))
+                xord(b)<<(8*i) for i,b in enumerate(unhexlify(data["rist_base"]))
             )
 
     if "imagine_twist" not in data:
diff --git a/src/per_curve/decaf.tmpl.c b/src/per_curve/decaf.tmpl.c
index 833f301..56b9d7f 100644
--- a/src/per_curve/decaf.tmpl.c
+++ b/src/per_curve/decaf.tmpl.c
@@ -776,7 +776,7 @@ decaf_bool_t API_NS(point_eq) ( const point_t p, const point_t q ) {
     gf_mul ( b, q->y, p->x );
     mask_t succ = gf_eq(a,b);
     
-    #if (COFACTOR == 8) && IMAGINE_TWIST
+    #if (COFACTOR == 8)
         gf_mul ( a, p->y, q->y );
         gf_mul ( b, q->x, p->x );
         #if !(IMAGINE_TWIST)
diff --git a/src/per_curve/point.tmpl.hxx b/src/per_curve/point.tmpl.hxx
index d481777..2e5c11d 100644
--- a/src/per_curve/point.tmpl.hxx
+++ b/src/per_curve/point.tmpl.hxx
@@ -305,7 +305,7 @@ public:
     */
     inline explicit Point(const FixedBlock<SER_BYTES> &buffer, bool allow_identity=true)
         /*throw(CryptoException)*/ {
-        if (DECAF_SUCCESS != decode(buffer,allow_identity ? DECAF_TRUE : DECAF_FALSE)) {
+        if (DECAF_SUCCESS != decode(buffer,allow_identity)) {
             throw CryptoException();
         }
     }
diff --git a/test/test_decaf.sage b/test/test_decaf.sage
index c2e7439..19e0490 100644
--- a/test/test_decaf.sage
+++ b/test/test_decaf.sage
@@ -10,6 +10,7 @@ p_tor4 = E.lift_x(-1)
 Tor = [p_tor4 * i for i in xrange(4)]
 q = 2^446-0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d
 FQ = GF(q)
+isoMagic = 1/sqrt(F(39082/39081)-1)
 
 passing = True
 
@@ -195,7 +196,16 @@ class DecafScalar():
         return True
 
 class DecafPoint():
-    _UNDER = c_uint64 * int(8*4)
+    @staticmethod
+    def _UNDER():
+        size = int(8*8*4)
+        alignment = 32
+        buf1 = bytearray(size+alignment-1)
+        buf2 = (c_char * int(size+alignment-1)).from_buffer(buf1)
+        raw_addr = addressof(buf2)
+        offset = (-raw_addr) % alignment
+        return (c_char*size).from_buffer(buf2,int(offset))
+    
     def __init__(self,cstruct=None,point=None):
         if cstruct is None:
             cstruct = DecafPoint._UNDER()
@@ -222,12 +232,11 @@ class DecafPoint():
     @staticmethod
     def _sage_deser(str):
         s = from_le(str)
-        if s > (F.cardinality()-1)/2: raise Exception("Point didn't decode")
+        if is_odd(s): raise Exception("Point didn't decode")
         if (s==0): return E(0)
         if not E.is_x_coord(s^2): raise Exception("Point didn't decode")
         P = E.lift_x(s^2)
-        t = P.xy()[1] / s
-        if is_odd(int(2*t/s)): P = -P
+        if is_odd(int(2*s^2*isoMagic/P.xy()[1])): P = -P
         return P
     
     def __eq__(self,other):
@@ -318,16 +327,16 @@ class DecafPoint():
         x,y = P.xy()
         s = sqrt(x)
         if s==0: return to_le(0,56)
-        if is_odd(int(2*y/s^2)): s = 1/s
-        if int(s) > (F.cardinality()-1)/2: s = -s
+        if is_odd(int(2*s^2*isoMagic/y)): s = 1/s
+        if is_odd(int(s)): s = -s
         return to_le(s,56)
         
     def _check(self):
         ss = self._sage_ser(self.point)
         cs = self._c_ser(self.cstruct)
         if ss != cs:
-            print ss
-            print cs
+            print "SAGE",b64encode(ss)
+            print "C   ",b64encode(cs)
             raise Exception("Check failed!")
         return True