diff --git a/src/coreclr/jit/rangecheck.cpp b/src/coreclr/jit/rangecheck.cpp
index 7d7e20fde9daff..277ec31f6fb2e6 100644
--- a/src/coreclr/jit/rangecheck.cpp
+++ b/src/coreclr/jit/rangecheck.cpp
@@ -996,8 +996,9 @@ void RangeCheck::MergeEdgeAssertions(Compiler*        comp,
                     return l2;
                 }
 
-                // Otherwise, prefer the BinOpArray(preferredBound) over the constant.
-                return l1;
+                // Otherwise, prefer the BinOpArray(preferredBound) over the constant for the upper bound
+                // and the constant for the lower bound.
+                return isLower ? l2 : l1;
             }
             unreached();
         };
diff --git a/src/coreclr/jit/rangecheck.h b/src/coreclr/jit/rangecheck.h
index d90257a990bc2e..8df2fc19ea791c 100644
--- a/src/coreclr/jit/rangecheck.h
+++ b/src/coreclr/jit/rangecheck.h
@@ -510,10 +510,15 @@ struct RangeOps
         {
             result.lLimit = r1lo;
         }
-        // Widen Upper Limit => Max(k, (a.len + n)) yields (a.len + n),
-        // This is correct if k >= 0 and n >= k, since a.len always >= 0
-        // (a.len + n) could overflow, but the result (a.len + n) also
+
+        // NOTE: in some of the calculations below, we assume that $bnd is never negative
+        // and we have to be careful by not masking possible overflows.
+
+        // Widen Upper Limit => Max(k, ($bnd + n)) yields ($bnd + n),
+        // This is correct if k >= 0 and n >= k, since $bnd always >= 0
+        // ($bnd + n) could overflow, but the result ($bnd + n) also
         // preserves the overflow.
+        //
         if (r1hi.IsConstant() && r1hi.GetConstant() >= 0 && r2hi.IsBinOpArray() &&
             r2hi.GetConstant() >= r1hi.GetConstant())
         {
@@ -524,14 +529,38 @@ struct RangeOps
         {
             result.uLimit = r1hi;
         }
+
+        // Rule: <$bnd + cns1, ...> U <cns2, ...> = <min(cns1, cns2), ...> when cns1 <= 0
+        //
+        // Example: <$bnd - 3, ...> U <0, ...> = <-3, ...>
+        //
+        if (r1lo.IsBinOpArray() && r2lo.IsConstant() && (r1lo.cns <= 0))
+        {
+            result.lLimit = Limit(Limit::keConstant, min(r1lo.cns, r2lo.cns));
+        }
+        if (r2lo.IsBinOpArray() && r1lo.IsConstant() && (r2lo.cns <= 0))
+        {
+            result.lLimit = Limit(Limit::keConstant, min(r2lo.cns, r1lo.cns));
+        }
+
+        // Rule: <..., $bnd + cns1> U <..., $bnd + cns2> = <..., $bnd + max(cns1, cns2)>
+        //
+        // Example: <..., $bnd + 10> U <..., $bnd + 20> = <..., $bnd + 20>
+        //
         if (r1hi.IsBinOpArray() && r2hi.IsBinOpArray() && r1hi.vn == r2hi.vn)
         {
-            result.uLimit = r1hi;
-            // Widen the upper bound if the other constant is greater.
-            if (r2hi.GetConstant() > r1hi.GetConstant())
-            {
-                result.uLimit = r2hi;
-            }
+            result.uLimit     = r1hi; // copy $bnd and kind info
+            result.uLimit.cns = max(r1hi.cns, r2hi.cns);
+        }
+
+        // Rule: <$bnd + cns1, ...> U <$bnd + cns2, ...> = <$bnd + min(cns1, cns2), ...>
+        //
+        // Example: <$bnd + 10, ...> U <$bnd + 20, ...> = <$bnd + 10, ...>
+        //
+        if (r1lo.IsBinOpArray() && r2lo.IsBinOpArray() && r1lo.vn == r2lo.vn)
+        {
+            result.lLimit     = r1lo; // copy $bnd and kind info
+            result.lLimit.cns = min(r1lo.cns, r2lo.cns);
         }
         return result;
     }