diff --git a/hledger-lib/Hledger/Data/Journal.hs b/hledger-lib/Hledger/Data/Journal.hs
index 94d551bc0..7168d48d7 100644
--- a/hledger-lib/Hledger/Data/Journal.hs
+++ b/hledger-lib/Hledger/Data/Journal.hs
@@ -583,16 +583,25 @@ checkBalanceAssertion p@Posting{pbalanceassertion=Just (BalanceAssertion{baamoun
                     | otherwise = []
 checkBalanceAssertion _ _ = Right ()
 
+-- | Does the difference between the asserted balance
+-- and (the corresponding part of) the actual balance
+-- appear as zero, when rendered to the greater of
+-- 1. the standard display precision for the commodity
+-- 2. the full precision of the asserted amount ?
+-- The posting is used when creating an error message.
 checkBalanceAssertionCommodity :: Posting -> Amount -> MixedAmount -> Either String ()
 checkBalanceAssertionCommodity p assertedamt actualbal
-  -- this effectively compares the actual balance rounded to display precision (I believe),
-  -- with the asserted balance as written. See examples in balance assertions manual.
   | isZeroAmount diff = Right ()
   | True              = Left err
     where
+      diff =
+        -- traceWith (("diff:"++).showAmountDebug) $
+        -- traceWith (("asserted:"++).showAmountDebug)
+        assertedamt -
+        -- traceWith (("actual:"++).showAmountDebug)
+        actualbalincommodity
       assertedcomm = acommodity assertedamt
       actualbalincommodity = fromMaybe nullamt $ find ((== assertedcomm) . acommodity) (amounts actualbal)
-      diff = assertedamt - actualbalincommodity
       diffplus | isNegativeAmount diff == False = "+"
                | otherwise = ""
       err = printf (unlines
diff --git a/hledger-lib/hledger_journal.m4.md b/hledger-lib/hledger_journal.m4.md
index 93e6a4884..ac997e3c6 100644
--- a/hledger-lib/hledger_journal.m4.md
+++ b/hledger-lib/hledger_journal.m4.md
@@ -468,10 +468,37 @@ flag or `real:` query.
 
 ### Assertions and precision
 
-The calculated account balance is rounded to display precision before checking.
-Eg: here the calculated balance is $1.006. The commodity directive causes
-users, and balance assertions, to see this rounded to two decimal places, ie $1.01,
-so this assertion passes:
+A commodity directive which limits the display precision, can affect assertions.
+
+In general, hledger balance assertions should pass or fail as you would
+expect from visual inspection and manual summing of the amounts shown
+in reports and error messages. 
+
+More specifically, assertions pass if the difference between asserted
+and actual amounts appears to be zero, when rendered to the greater of
+the standard display precision and the asserted amount's precision.
+
+Here are some examples of this in action.
+
+Asserting the exact balance:
+```journal
+commodity $1000.00
+
+2019/01/01
+    (a)             $0.006
+
+2019/01/02
+    (a)             $1.00  = $1.006
+
+; Actual balance:       1.006
+; Asserted balence:     1.006
+; Difference:           0.000
+; Standard & asserted precisions: 2, 3
+; Difference rendered:  0.000
+; Result:               pass
+```
+
+Asserting the balance rounded to fewer decimal places:
 ```journal
 commodity $1000.00
 
@@ -480,9 +507,16 @@ commodity $1000.00
 
 2019/01/02
     (a)             $1.00  = $1.01
+
+; Actual balance:       1.006
+; Asserted balence:     1.01
+; Difference:           0.004
+; Standard & asserted precisions: 2, 2
+; Difference rendered:  0.00
+; Result:               pass
 ```
 
-The asserted balance is not rounded to display precision. So this assertion fails:
+Asserting an inexact balance with too many decimal places (fails):
 ```journal
 commodity $1000.00
 
@@ -490,9 +524,14 @@ commodity $1000.00
     (a)             $0.006
 
 2019/01/02
-    (a)             $1.00  = $1.007
-# calculated: $1.01
-# asserted:   $1.007 (difference: +$0.001)
+    (a)             $1.00  = $1.0061
+
+; Actual balance:       1.006
+; Asserted balence:     1.0061
+; Difference:           0.0001
+; Standard & asserted precisions: 2, 4
+; Difference rendered:  0.0001
+; Result:               fail
 ```
 
 ## Balance Assignments
diff --git a/tests/journal/balance-assertions.test b/tests/journal/balance-assertions.test
index 5b52d86a4..2a42bbd74 100755
--- a/tests/journal/balance-assertions.test
+++ b/tests/journal/balance-assertions.test
@@ -366,9 +366,38 @@ hledger -f- stats
 >>>2 /unexpected '@'/
 >>>=1
 
-# 21. The calculated balance is rounded to display precision before checking.
-# Here the calculated balance is $1.005 but users, and balance assertions,
-# see it as $1.00 (because the commodity directive set display precision to 2).
+# 21. With a commodity directive limiting the display precision. 
+# Assertions pass if the difference between asserted and actual amounts
+# appears to be zero, when rendered to the greater of the standard 
+# display precision and the asserted amount's precision. 
+# Here,
+# Actual balance:       1.006
+# Asserted balence:     1.006
+# Difference:           0.000
+# Standard & asserted precisions: 2, 3
+# Difference rendered:  0.000
+# Result:               pass
+hledger -f- stats
+<<<
+commodity $1000.00
+
+2019/01/01
+    (a)             $0.006
+
+2019/01/02
+    (a)             $1.00  = $1.006
+
+>>> /Transactions/
+>>>2
+>>>=0
+
+# 22. A rounded assertion amount can also pass. Here,
+# Actual balance:       1.006
+# Asserted balence:     1.01
+# Difference:           0.004
+# Standard & asserted precisions: 2, 2
+# Difference rendered:  0.00
+# Result:               pass
 hledger -f- stats
 <<<
 commodity $1000.00
@@ -383,7 +412,13 @@ commodity $1000.00
 >>>2
 >>>=0
 
-# 22. The asserted balance is not rounded to display precision.
+# 23. A more precise assertion amount can fail. Here,
+# Actual balance:       1.006
+# Asserted balence:     1.0061
+# Difference:           0.0001
+# Standard & asserted precisions: 2, 4
+# Difference rendered:  0.0001
+# Result:               fail
 hledger -f- stats
 <<<
 commodity $1000.00
@@ -392,8 +427,8 @@ commodity $1000.00
     (a)             $0.006
 
 2019/01/02
-    (a)             $1.00  = $1.007
+    (a)             $1.00  = $1.0061
 
 >>>
->>>2 /difference: \+\$0\.001/
+>>>2 /difference: \+\$0\.0001/
 >>>=1