diff --git a/lslopt/lsloutput.py b/lslopt/lsloutput.py
index 1ea9658..39fdd96 100644
--- a/lslopt/lsloutput.py
+++ b/lslopt/lsloutput.py
@@ -26,11 +26,11 @@ debugScopes = False
 
 class outscript(object):
 
-    binary_operands = frozenset(('||','&&','^','|','&','==','!=','<','<=','>',
+    binary_operators = frozenset(('||','&&','^','|','&','==','!=','<','<=','>',
         '>=','<<','>>','+','-','*','/','%', '=', '+=', '-=', '*=', '/=','%=',
         ))
     extended_assignments = frozenset(('&=', '|=', '^=', '<<=', '>>='))
-    unary_operands = frozenset(('NEG', '!', '~'))
+    unary_operators = frozenset(('NEG', '!', '~'))
     op_priority = {'=':0, '+=':0, '-=':0, '*=':0, '/=':0, '%=':0, '&=':0,
         '|=':0, '^=':0, '<<=':0, '>>=':0,
         '||':1, '&&':1, '|':2, '^':3, '&':4, '==':5, '!=':5,
@@ -216,7 +216,7 @@ class outscript(object):
         nt = expr.nt
         child = expr.ch
 
-        if nt in self.binary_operands:
+        if nt in self.binary_operators:
             lnt = child[0].nt
             lparen = False
             rnt = child[1].nt
@@ -237,7 +237,8 @@ class outscript(object):
                     lparen = True
 
                 # This situation has ugly cases due to the strange precedence
-                # of unary minus. Consider the following two statements:
+                # of unary minus. Consider the following two statements, paying
+                # attention to the binding power of the binary not ~ operator:
                 #     (~-a) * a
                 #     a * (~-a) * a
                 # In one case, the (~-a) is a left child; in the other, it's
@@ -246,20 +247,44 @@ class outscript(object):
                 #     ~-(a * a)
                 #     a * ~-(a * a)
                 # Yet the tree structure makes it quite hard to detect these.
-                # So as a safeguard, for now we parenthesize all ~ and ! within
-                # binary operands, as they have a deceitful binding power when
-                # there's a unary minus downstream.
-                #
-                # TODO: See if the parenthesizing of ~ and ! can be improved.
+                # We have to descend down the left nodes as we keep finding
+                # binary operators or unary operators, to find whether the
+                # symbol is followed by unary minus. If that's the case, we
+                # need to act as if there was a negation right here.
                 elif lnt in ('~', '!'):
-                    lparen = True
+                    lnode = child[0]
+                    while True:
+                        lnode = lnode.ch[0]
+                        if (lnode.nt not in self.op_priority
+                            and lnode.nt not in ('~', '!')
+                           ):
+                            break
+                    if lnode.nt == 'NEG' and base_pri > self.op_priority['-']:
+                        lparen = True
 
                 if rnt in self.op_priority:
                     if self.op_priority[rnt] <= base_pri:
                         rparen = True
+                elif rnt == 'NEG' and self.op_priority['-'] < base_pri:
+                    rparen = True
                 # see above
                 elif rnt in ('~', '!'):
-                    rparen = True
+                    lnode = child[1]
+                    while True:
+                        # Descend down the left nodes of the right node, to
+                        # find whether it's immediately followed by -
+                        lnode = lnode.ch[0]
+                        if lnode.nt not in self.op_priority and lnode.nt not in ('~', '!'):
+                            break
+                    if lnode.nt == 'NEG' and base_pri > self.op_priority['-']:
+                        # TODO: Improve right operand parenthesis removal
+                        #       for minus signs.
+                        # Shouldn't this look into the RHS node?
+                        #       a * -b * c
+                        # is currently translated to
+                        #       a * (-b * c)
+                        # which is correct but not optimal.
+                        rparen = True
 
             if lparen:
                 ret = '(' + self.OutExpr(child[0]) + ')'
@@ -328,7 +353,7 @@ class outscript(object):
         if nt == 'PRINT':
             return 'print(' + self.OutExpr(child[0]) + ')'
 
-        if nt in self.unary_operands:
+        if nt in self.unary_operators:
             ret = nt
             lnt = child[0].nt
             paren = False
diff --git a/unit_tests/coverage.suite/lslparse-2.out b/unit_tests/coverage.suite/lslparse-2.out
index af53bdd..0327ec8 100644
--- a/unit_tests/coverage.suite/lslparse-2.out
+++ b/unit_tests/coverage.suite/lslparse-2.out
@@ -15,9 +15,9 @@ default
         list L;
         f += (float)i;
         L += (list)((integer)((float)i));
-        i = (~(integer)-2) * 3;
-        i = (~(integer)-2.) * 3;
-        i = (~(integer)(-i)) * 3;
+        i = ~(integer)-2 * 3;
+        i = ~(integer)-2. * 3;
+        i = ~(integer)(-i) * 3;
         "" + (string)((key)"");
         (string)((key)"") + "";
         @J;
diff --git a/unit_tests/expr.suite/opts.out b/unit_tests/expr.suite/opts.out
index 64ac0f4..c00c5ee 100644
--- a/unit_tests/expr.suite/opts.out
+++ b/unit_tests/expr.suite/opts.out
@@ -23,9 +23,9 @@
 , 3 + llGetLinkNumber()
 , ~llGetLinkNumber()
 , llGetLinkNumber()
-, -((~-~llGetLinkNumber()) + (~-~llGetLinkNumber()))
-, -~-~llGetLinkNumber() + (~-~-llGetLinkNumber())
-, (~-~-llGetLinkNumber()) + (~-~-llGetLinkNumber())
+, -(~-~llGetLinkNumber() + ~-~llGetLinkNumber())
+, -~-~llGetLinkNumber() + ~-~-llGetLinkNumber()
+, ~-~-llGetLinkNumber() + ~-~-llGetLinkNumber()
 , 5 + llGetLinkNumber() + (5 + llGetLinkNumber())
 , 0
 ]
\ No newline at end of file
diff --git a/unit_tests/regression.suite/boolean-and.out b/unit_tests/regression.suite/boolean-and.out
index 78bd935..8d9cb52 100644
--- a/unit_tests/regression.suite/boolean-and.out
+++ b/unit_tests/regression.suite/boolean-and.out
@@ -5,7 +5,7 @@ default
         string s = llGetObjectDesc();
         key k = llGenerateKey();
         integer i = llGetLinkNumber();
-        if (!((!(s == "A")) | k == llGenerateKey() | (~llSubStringIndex(s, "B"))))
+        if (!(!(s == "A") | k == llGenerateKey() | ~llSubStringIndex(s, "B")))
             llDie();
         if (-!(i ^ 5 | i ^ 9) & llGetLinkNumber())
             llDie();
diff --git a/unit_tests/regression.suite/parens.lsl b/unit_tests/regression.suite/parens.lsl
index d39b159..ad177e9 100644
--- a/unit_tests/regression.suite/parens.lsl
+++ b/unit_tests/regression.suite/parens.lsl
@@ -1 +1,17 @@
-(-3)*4 | -(3*4) | ~-3*4 | -~3*4 | ~(-3)*4 & (-(~3)*4 | -~(3*4)) | - -3
+[ (-3) * 4
+, -3 * 4
+, -(3 * 4)
+, ~-3 * 4
+, -~3 * 4 | (~(-3) * 4 & (-(~3)*4 | -~(3 * 4))) | - -3
+, (3 * ~-4) * 5
+, 3 * ~-4 * 5
+, 3 * (~-4) * 5
+, 3 * ~(-4) * 5
+, 3 * ~(-4 * 5)
+, 3 * (-~4) * 5
+, 3 * -(~4) * 5
+, 3 * -(~4 * 5)
+, 3 * -~(4 * 5)
+, 0 * (-1e20) * 1e20
+, 0 * -1e20 * 1e20
+]
diff --git a/unit_tests/regression.suite/parens.out b/unit_tests/regression.suite/parens.out
index 1788564..6c18bab 100644
--- a/unit_tests/regression.suite/parens.out
+++ b/unit_tests/regression.suite/parens.out
@@ -1 +1,17 @@
-(-3) * 4 | -3 * 4 | (~-3 * 4) | -(~3) * 4 | (~-3) * 4 & (-(~3) * 4 | -~(3 * 4)) | - -3
\ No newline at end of file
+[ (-3) * 4
+, -3 * 4
+, -3 * 4
+, ~-3 * 4
+, -~3 * 4 | (~-3) * 4 & (-~3 * 4 | -~(3 * 4)) | - -3
+, 3 * (~-4) * 5
+, 3 * (~-4 * 5)
+, 3 * (~-4) * 5
+, 3 * (~-4) * 5
+, 3 * (~-4 * 5)
+, 3 * (-~4) * 5
+, 3 * (-~4 * 5)
+, 3 * (-~4 * 5)
+, 3 * (-~(4 * 5))
+, 0 * (-1e20) * 1e20
+, 0 * (-1e20 * 1e20)
+]
\ No newline at end of file