diff --git a/frontend/document/credocument.lua b/frontend/document/credocument.lua
index 290ec7caa..a8b52029c 100644
--- a/frontend/document/credocument.lua
+++ b/frontend/document/credocument.lua
@@ -305,12 +305,20 @@ function CreDocument:_readMetadata()
 end
 
 function CreDocument:close()
-    if self.buffer then
-        self.buffer:free()
-        self.buffer = nil
-    end
+    -- Let Document do the refcount check, and tell us if we actually need to tear down the instance.
+    if Document.close(self) then
+        -- Yup, final Document instance, we can safely destroy internal data.
+        -- (Document already took care of our self._document userdata).
+        if self.buffer then
+            self.buffer:free()
+            self.buffer = nil
+        end
 
-    Document.close(self)
+        -- Only exists if the call cache is enabled
+        if self._callCacheDestroy then
+            self._callCacheDestroy()
+        end
+    end
 end
 
 function CreDocument:updateColorRendering()
@@ -1742,12 +1750,6 @@ function CreDocument:setupCallCache()
     if do_stats then
         self.close = function(_self)
             dumpStats()
-            _self._callCacheDestroy()
-            CreDocument.close(_self)
-        end
-    else
-        self.close = function(_self)
-            _self._callCacheDestroy()
             CreDocument.close(_self)
         end
     end
diff --git a/frontend/document/document.lua b/frontend/document/document.lua
index 5f30b60b1..d4b6c45e4 100644
--- a/frontend/document/document.lua
+++ b/frontend/document/document.lua
@@ -92,21 +92,29 @@ end
 
 -- this might be overridden by a document implementation
 -- (in which case, do make sure it calls this one, too, to avoid refcounting mismatches in DocumentRegistry!)
+-- Returns true if the Document instance needs to be destroyed (no more live refs),
+-- false if not (i.e., we've just decreased the refcount, so, leave internal engine data alone).
+-- nil if all hell broke loose.
 function Document:close()
     local DocumentRegistry = require("document/documentregistry")
     if self.is_open then
-        if DocumentRegistry:closeDocument(self.file) == 0 then
+        local refcount = DocumentRegistry:closeDocument(self.file)
+        if refcount == 0 then
             self.is_open = false
             self._document:close()
             self._document = nil
 
             -- NOTE: DocumentRegistry:openDocument will force a GC sweep the next time we open a Document.
             --       MµPDF will also do a bit of spring cleaning of its internal cache when opening a *different* document.
+            return true
         else
-            logger.warn("Tried to close a document with *multiple* remaining hot references")
+            -- This can happen in perfectly sane contexts (i.e., Reader -> History -> View fullsize cover on the *same* book).
+            logger.dbg("Document: Decreased refcount to", refcount, "for", self.file)
+            return false
         end
     else
-        logger.warn("Tried to close an already closed document")
+        logger.warn("Tried to close an already closed document:", self.file)
+        return nil
     end
 end
 
diff --git a/frontend/document/documentregistry.lua b/frontend/document/documentregistry.lua
index ef7b1d451..36e4720fa 100644
--- a/frontend/document/documentregistry.lua
+++ b/frontend/document/documentregistry.lua
@@ -214,6 +214,7 @@ function DocumentRegistry:openDocument(file, provider)
         end
     else
         self.registry[file].refs = self.registry[file].refs + 1
+        logger.dbg("DocumentRegistry: Increased refcount to", self.registry[file].refs, "for", file)
     end
     if self.registry[file] then
         return self.registry[file].doc
@@ -232,7 +233,16 @@ function DocumentRegistry:closeDocument(file)
             return self.registry[file].refs
         end
     else
-        error("Try to close unregistered file.")
+        error("Tried to close an unregistered file.")
+    end
+end
+
+--- Queries the current refcount for a given file
+function DocumentRegistry:getReferenceCount(file)
+    if self.registry[file] then
+        return self.registry[file].refs
+    else
+        return nil
     end
 end
 
diff --git a/frontend/document/pdfdocument.lua b/frontend/document/pdfdocument.lua
index 3cd0d4874..4130b321b 100644
--- a/frontend/document/pdfdocument.lua
+++ b/frontend/document/pdfdocument.lua
@@ -261,9 +261,16 @@ function PdfDocument:writeDocument()
 end
 
 function PdfDocument:close()
-    if self.is_edited then
-        self:writeDocument()
+    -- NOTE: We can't just rely on Document:close's return code for that, as we need self._document
+    --       in :writeDocument, and it would have been destroyed.
+    local DocumentRegistry = require("document/documentregistry")
+    if DocumentRegistry:getReferenceCount(self.file) == 1 then
+        -- We're the final reference to this Document instance.
+        if self.is_edited then
+            self:writeDocument()
+        end
     end
+
     Document.close(self)
 end
 
diff --git a/frontend/document/picdocument.lua b/frontend/document/picdocument.lua
index 7a58aa05d..1422a7481 100644
--- a/frontend/document/picdocument.lua
+++ b/frontend/document/picdocument.lua
@@ -22,6 +22,7 @@ function PicDocument:init()
         error("Failed to open image:" .. self._document)
     end
 
+    self.is_open = true
     self.info.has_pages = true
     self.info.configurable = false
 
diff --git a/plugins/statistics.koplugin/main.lua b/plugins/statistics.koplugin/main.lua
index d2f9d208a..7690dad5c 100644
--- a/plugins/statistics.koplugin/main.lua
+++ b/plugins/statistics.koplugin/main.lua
@@ -122,7 +122,7 @@ local monthTranslation = {
 }
 
 function ReaderStatistics:isDocless()
-    return self.ui == nil or self.ui.document == nil
+    return self.ui == nil or self.ui.document == nil or self.ui.document.is_pic == true
 end
 
 -- NOTE: This is used in a migration script by ui/data/onetime_migration,
@@ -139,9 +139,10 @@ ReaderStatistics.default_settings = {
 }
 
 function ReaderStatistics:init()
-    if not self:isDocless() and self.ui.document.is_pic then
+    if self:isDocless() then
         return
     end
+
     self.start_current_period = os.time()
     self:resetVolatileStats()