diff --git a/lib/core/test/unit/Cardano/Wallet/Primitive/CoinSelection/MA/RoundRobinSpec.hs b/lib/core/test/unit/Cardano/Wallet/Primitive/CoinSelection/MA/RoundRobinSpec.hs
index 851ce593aff..72309842e17 100644
--- a/lib/core/test/unit/Cardano/Wallet/Primitive/CoinSelection/MA/RoundRobinSpec.hs
+++ b/lib/core/test/unit/Cardano/Wallet/Primitive/CoinSelection/MA/RoundRobinSpec.hs
@@ -501,11 +501,11 @@ prop_AssetCount_TokenMap_placesEmptyMapsFirst maps =
         $ cover 20 (emptyMapCount >= 8 && nonEmptyMapCount >= 8)
             "empty map count >= 8 && non-empty map count >= 8"
         -- Check head and last element of list:
-        $ cover 40 (isEmptyMap $ NE.head maps)
+        $ cover 20 (isEmptyMap $ NE.head maps)
             "head element is empty map"
         $ cover 40 (not $ isEmptyMap $ NE.head maps)
             "head element is non-empty map"
-        $ cover 40 (isEmptyMap $ NE.last maps)
+        $ cover 20 (isEmptyMap $ NE.last maps)
             "last element is empty map"
         $ cover 40 (not $ isEmptyMap $ NE.last maps)
             "last element is non-empty map"
@@ -738,7 +738,7 @@ prop_performSelection_small minCoinValueFor costFor (Blind (Small criteria)) =
     prop_performSelection minCoinValueFor costFor (Blind criteria) $ \result ->
         cover 10 (selectionUnlimited && selectionSufficient result)
             "selection unlimited and sufficient"
-        . cover 5 (selectionLimited && selectionSufficient result)
+        . cover 4 (selectionLimited && selectionSufficient result)
             "selection limited but sufficient"
         . cover 10 (selectionLimited && selectionInsufficient result)
             "selection limited and insufficient"
diff --git a/lib/core/test/unit/Cardano/Wallet/Primitive/Types/TokenMapSpec.hs b/lib/core/test/unit/Cardano/Wallet/Primitive/Types/TokenMapSpec.hs
index 0c497163bb4..8ed0f6fef86 100644
--- a/lib/core/test/unit/Cardano/Wallet/Primitive/Types/TokenMapSpec.hs
+++ b/lib/core/test/unit/Cardano/Wallet/Primitive/Types/TokenMapSpec.hs
@@ -773,9 +773,9 @@ prop_equipartitionQuantitiesWithUpperBound_coverage
     :: TokenMap -> Positive TokenQuantity -> Property
 prop_equipartitionQuantitiesWithUpperBound_coverage m (Positive maxQuantity) =
     checkCoverage $
-    cover 8 (maxQuantity == TokenQuantity 1)
+    cover 4 (maxQuantity == TokenQuantity 1)
         "Maximum allowable quantity == 1" $
-    cover 8 (maxQuantity == TokenQuantity 2)
+    cover 4 (maxQuantity == TokenQuantity 2)
         "Maximum allowable quantity == 2" $
     cover 8 (maxQuantity >= TokenQuantity 3)
         "Maximum allowable quantity >= 3" $
diff --git a/lib/core/test/unit/Cardano/Wallet/Primitive/Types/UTxOIndexSpec.hs b/lib/core/test/unit/Cardano/Wallet/Primitive/Types/UTxOIndexSpec.hs
index 2eb6a8f0246..91758ee1ca0 100644
--- a/lib/core/test/unit/Cardano/Wallet/Primitive/Types/UTxOIndexSpec.hs
+++ b/lib/core/test/unit/Cardano/Wallet/Primitive/Types/UTxOIndexSpec.hs
@@ -433,11 +433,11 @@ prop_selectRandom_one_withAdaOnly u = checkCoverage $ monadicIO $ do
 prop_selectRandom_one_withAsset :: UTxOIndex -> AssetId -> Property
 prop_selectRandom_one_withAsset u a = checkCoverage $ monadicIO $ do
     result <- run $ UTxOIndex.selectRandom u (WithAsset a)
-    monitor $ cover 70 (a `Set.member` UTxOIndex.assets u)
+    monitor $ cover 50 (a `Set.member` UTxOIndex.assets u)
         "index has the specified asset"
-    monitor $ cover 70 (Set.size (UTxOIndex.assets u) > 1)
+    monitor $ cover 50 (Set.size (UTxOIndex.assets u) > 1)
         "index has more than one asset"
-    monitor $ cover 70 (isJust result)
+    monitor $ cover 50 (isJust result)
         "selected an entry"
     case result of
         Nothing ->
@@ -459,11 +459,11 @@ prop_selectRandom_one_withAsset u a = checkCoverage $ monadicIO $ do
 prop_selectRandom_one_withAssetOnly :: UTxOIndex -> AssetId -> Property
 prop_selectRandom_one_withAssetOnly u a = checkCoverage $ monadicIO $ do
     result <- run $ UTxOIndex.selectRandom u (WithAssetOnly a)
-    monitor $ cover 70 (a `Set.member` UTxOIndex.assets u)
+    monitor $ cover 50 (a `Set.member` UTxOIndex.assets u)
         "index has the specified asset"
-    monitor $ cover 70 (Set.size (UTxOIndex.assets u) > 1)
+    monitor $ cover 50 (Set.size (UTxOIndex.assets u) > 1)
         "index has more than one asset"
-    monitor $ cover 20 (isJust result)
+    monitor $ cover 10 (isJust result)
         "selected an entry"
     case result of
         Nothing ->
@@ -509,11 +509,11 @@ prop_selectRandom_all_withAdaOnly u = checkCoverage $ monadicIO $ do
 prop_selectRandom_all_withAsset :: UTxOIndex -> AssetId -> Property
 prop_selectRandom_all_withAsset u a = checkCoverage $ monadicIO $ do
     (selectedEntries, u') <- run $ selectAll (WithAsset a) u
-    monitor $ cover 70 (a `Set.member` UTxOIndex.assets u)
+    monitor $ cover 50 (a `Set.member` UTxOIndex.assets u)
         "index has the specified asset"
-    monitor $ cover 70 (Set.size (UTxOIndex.assets u) > 1)
+    monitor $ cover 50 (Set.size (UTxOIndex.assets u) > 1)
         "index has more than one asset"
-    monitor $ cover 70 (not (null selectedEntries))
+    monitor $ cover 50 (not (null selectedEntries))
         "selected at least one entry"
     assert $ L.all (\(_, o) -> not (txOutHasAsset o a)) (UTxOIndex.toList u')
     assert $ L.all (\(_, o) -> txOutHasAsset o a) selectedEntries
@@ -526,11 +526,11 @@ prop_selectRandom_all_withAsset u a = checkCoverage $ monadicIO $ do
 prop_selectRandom_all_withAssetOnly :: UTxOIndex -> AssetId -> Property
 prop_selectRandom_all_withAssetOnly u a = checkCoverage $ monadicIO $ do
     (selectedEntries, u') <- run $ selectAll (WithAssetOnly a) u
-    monitor $ cover 70 (a `Set.member` UTxOIndex.assets u)
+    monitor $ cover 50 (a `Set.member` UTxOIndex.assets u)
         "index has the specified asset"
-    monitor $ cover 70 (Set.size (UTxOIndex.assets u) > 1)
+    monitor $ cover 50 (Set.size (UTxOIndex.assets u) > 1)
         "index has more than one asset"
-    monitor $ cover 20 (not (null selectedEntries))
+    monitor $ cover 10 (not (null selectedEntries))
         "selected at least one entry"
     assert $ all (\(_, o) -> not (txOutHasAssetOnly o a)) (UTxOIndex.toList u')
     assert $ all (\(_, o) -> txOutHasAssetOnly o a) selectedEntries
diff --git a/lib/core/test/unit/Cardano/Wallet/Primitive/TypesSpec.hs b/lib/core/test/unit/Cardano/Wallet/Primitive/TypesSpec.hs
index 63ee7902611..da27ac504f1 100644
--- a/lib/core/test/unit/Cardano/Wallet/Primitive/TypesSpec.hs
+++ b/lib/core/test/unit/Cardano/Wallet/Primitive/TypesSpec.hs
@@ -1149,7 +1149,9 @@ instance Arbitrary TxOut where
     -- No Shrinking
     arbitrary = TxOut
         <$> arbitrary
-        <*> fmap TokenBundle.fromCoin genCoin
+        -- Here we deliberately restrict the range of coins in order to increase
+        -- the probability of collisions between identical transaction outputs:
+        <*> fmap TokenBundle.fromCoin (scale (`mod` 8) genCoin)
 
 instance Arbitrary TxIn where
     -- No Shrinking